for me, i did sqrt(18)-sqrt(8) is (sqrt(9)*sqrt(2))-(sqrt(4)*sqrt(2)) that is sqrt(2(sqrt(9)-sqrt(4))) that is sqrt(2(3-2)) that is sqrt(2*1) that is sqrt(2)
@@7MinutozRapsLetrashey could you help me understand the step of sqrt(2(sqrt(9)-sqrt(4))) I don’t understand how you got there from (sqrt(9)*sqrt(2)) - (sqrt(4)*sqrt(2))
@@marquis5178 im sorry this was almost a year ago and i dont remember my own maths 💀 Wait i remember So, when you have, lets say sqrt(4) You could do sqrt(2)*sqrt(2)=sqrt(2*2) = sqrt(4) Basically, its sqrt(x*y) = sqrt(x)*sqrt(y)
@s5178The problem is partially due to a typo problem: when 7MRL typed _sqrt(2(sqrt(9)-sqrt(4)))_ they probably meant _sqrt(2)(sqrt(9)-sqrt(4))_ i.e. they got the shared factor _sqrt(2)_ out of the parentheses. And because _sqrt(9)-sqrt(4)_ is 1, the equality's stayed correct, despite the typo braking down the reasoning.
You can also do it this way. If you notice that the radicands multiply to a perfect square, solve it algebraically by squaring both sides. So initially, the problem is sqrt(20) - sqrt(5) = x. When squaring both sides, you end up with sqrt(20)^2 - 2*sqrt(20*5) + (- sqrt(5))^2 = x^2. This yields 20 - 20 + 5 = x^2 or 5 = x^2. We know the solution is positive since sqrt(20) - sqrt(5) is positive, so we can ignore the negative solution to this quadratic, so the solution is x = sqrt(5).
@@daapdary while it is true that given x^2 = 20, x = +- 2*sqrt(5), the notation sqrt(x) assumes the positive result only. It's convention. That's why if you plug x = sqrt(20) into wolframalpha or sqrt(20) into calculator, it will only give the positive value.
@@theeternalsw0rd Good point, thanks! So, sqrt(144) is positive in my example, but if I had started with 144 and then took the square root, it would be ± sqrt(144). The convention makes sense: a square root _function_ (where the domain is nonnegative real numbers) might as well return the nonnegative square root.
This man explained it so well, but it didn't have to be so lengthy. This could've been done by prime factorization and grouping the factors into groups of two.
@@bettygilliland456 Prime factors don't have to remembered in general, just the rules for divisibility for small primes (mainly 2, 3, and 5). Successively applying that (or doing a little more work for higher primes) gets you the factorization.
@@bettygilliland456You don't need to remember anything to factor 20. In fact if you can't factor 20 you should not be doing this problem. Math is not about "know how to solve a problem". It's all about "find the solution yourself". If you lack some critical skill that is needed for this level of problem, it's better to consolidate that first.
This is a nice trick to know. Back in school I used to just put everything into a bracket and multiply it with itself so it would be something like (a-b)^2 which equals a^2 - 2ab +b^2 and then apply square root to this result; this way you get rid of the square root and ab would always give you a perfect square. If ab is not a perfect square this technique wouldnt work but neither would his.
Thought process: 2 is the square root of 4, so the square root of 5 is close to 2. 4 is the square root of 16 but since that is a bit further away from 20, changing the number to 4.5 is a bit over 20 so that works. 4.5 - 2 =2.5 Now since the answer asks for a square root, that number must be squared. 2.5 × 2.5 is around and closest to 5. Final answer: square root 5.
For the tryout question, the answer is "D", square root of 2. Square root of 18 is the same as 3 root 2, and square root of 8 is 2 root 2. 3 root 2 - 2 root 2 gives you root 2.
This is the kind of problem that seems tricky when you first glance at it, but is trivial when you think about it for a few seconds. It is ironic how things can be that way, that what you think is tricky is really simple, or conversely, what you think is simple is really quite tricky.
@UCxNMlPEiqKVeZZ6I8q_nJww There are some high-school students where I would be relieved if they could find the state that Chicago is in, on a map of the U.S., or tell you what year that the War of 1812 took place. So am joyful if they can solve this little math problem easily, which I am sure some can, and by rights, most of them should be able
thought process: A = sqrt(20) - sqrt(5) A^2 = (sqrt(20) - sqrt(5))^2 We can use a^2-2ab^-b^2 sqrt(20)^2 - 2 * sqrt(20 x 5) + sqrt(5)^2 20 - 2 * 10 + 5 A^2 = 5 sqrt(A^2)= sqrt(5) mine seem to be different from others
The other way to do it without recalling the mathmatical relationhship of breaking out a square root under the radical is: Simply estimate the square root of 20 which is between 4 and 5...let's call it 4.5. Then do basic square root of 5 in your head and say that is ~ 2.2 Perform 4.5-2.2 = 2.2 or 2.3 and square it...again in your head = 5 So answer is square root of 5. This is made possible by multiple choice doing basic arithmetic in your head aka deduction. Of course, the mathematical answer is pretty well known as well for people that passed math class and I have had a lot of calculus so not a big deal...lol.
Another thought process In this case, we can think with bounding the values. Now that the perfect square roots are written down, you can evaluate that 4 < sqrt(20) < 5, and 2 < sqrt(5) < 3, so the answer is roughly 2, which in this case only corresponds with sqrt(5). In tests like SAT, where you are given answers to choose from, and not specific values, this can be nice to use. This can also help in general when you need to estimate the value of a square root, like sqrt(55) would be between 7 and 8. Edit: for the bonus question, sqrt(18) is slightly above 4, and sqrt(8) is slightly below 3, so the answer would be slightly above 1, which in this case is ~1.4 = sqrt(2)
I just did a bunch of aproximations and got it wright from that Edit to explain. I knew that square root of 20 would be a little under 4.5 (after checking work later its 4.472) And i knew square root of 5 is under 2.5 but i knew it was more under 2.5 then the other number was under 4.5 so wighted it by making it 2.3. 4.5-2.3=2.2 thus logically square root of 5 was the closest.
My try before seeing: sqrt(20) can be written as sqrt(4) x sqrt(5) So our expression now is sqrt(5)*sqrt(4) - sqrt(5) Factor out sqrt(5) sqrt(5) ( sqrt(4) - 1) sqrt(5) ( 2 - 1 ) sqrt(5) (1) sqrt(5) Hope am correct
sqrt(20) is something between 4 and 5, sqrt(5) is something between 2 and 3, so subtracting the two should give you something pretty close to 2. sqrt(15) is almost 4, so that's out. sqrt(10) is more than 3, so that's out. sqrt(5) is between 2 and 3, so a possibility. sqrt(2.5) is less than 2, so that's out. Only the square root of 5 is in the expected ballpark, so that's gotta be it.
@@ES-hr6vg Because the idea of factoring the radicand doesn't always occur to some of us ;-) All the more so in a case like this where the numbers involved are all small enough that the closest perfect squares are trivial enough to do the estimations indicated.
My method :- We begin by taking the square of the expression. (√20 - √5)^2 = 20 + 5 - 2 ( √100) [ By using the formula = ( a - b)^2 = a^2 + b^2 - 2ab =20 +5 - 2(10) =25-20 =5 = If, (√20 - √5)^2 = 5, then = √20 - √5 = √5
I just did it by approximation. 4^2 and 5^2 are 16 and 25, so sqrt of 20 should be around 4.5, apply same logic to sqrt of 5 and you get around 2.2, so the answer is approx 2.3. srqt 5 seems closest to 2.3.
The multiple choice answers also make it way too obvious, since 15 and 10 are bigger than 3 squared and 2.5 is smaller than 2 squared. Sqrt of 5 is the only one that's even in the ballpark.
I looked at the thumbnail and solved it in less than a minute. It's really not that bad, it was easier for me cause I've been doing some review on this before school starts and may be more familiar with this at first glance. Otherwise, I don't see why it would seem like a hard SAT question.
Using his method on the second equation, you can break down the sqrt(18) into sqrt(9)*sqrt(2) (you can also break it down into 3 and 6, but they aren't perfect squares, so they're not helpful) You can also break down the sqrt(8) into sqrt(4)*sqrt(2). Both 9 and 4 are perfect squares, so you end up with 3*sqrt(2)-2*sqrt(2). It becomes a simple case of 3-2=1, and you're left with sqrt(2), making the answer D.
We can see that sqrt(20) is between 4 and 5, and that 20 is 4 more than 16 but 5 less than 25, putting it at approximately 4+4/9, or 4.44. And, we can see that sqrt(5) is between 2 and 3, and that 5 is 1 more than 4 but 4 less than 9, putting it at approximately 2+1/5, or 2.2. If you want a formula for that, it's LB + (MT / (MT+LT)), where: LB = The lower bound of possible values. MT = The "more than" value, or how much more the parameter of the function is than the square of the lower bound. LT = The "less than" value, or how much less the parameter of the function is than the square of the upper bound. It's only an approximation, but it's more than enough to do a multiple choice question like this in your head. In the case of sqrt(20), LB = 4, MT = 4, LT = 5, so we get 4+4/9. In the case of sqrt(5), LB = 2, MT = 1, LT = 4, so we get 2+1/5. Thus, sqrt(20) - sqrt(5) is approximately 4.44 - 2.2, or 2.24, which is incidentally the exact value of sqrt(5) to 2 decimal places, so it's pretty safe to say the answer is C. EDIT: Oh, and applying this to the bonus question: sqrt(18): LB = 4, MT = 2, LT = 7, so it is approximately 4+2/9, or 4.22 sqrt(8): LB = 2, MT = 4, LT = 1, so it is approximately 2+4/5, or 2.8 Thus, sqrt(18) - sqrt(8) is approximately 4.22 - 2.8, or 1.42, which I probably don't need to tell you is pretty darn close to sqrt(2), so the answer to that is D.
I have a good and very simple method for my students. If we want to add or subtract any two square roots, we need to use two rules. (BTW, we can do that with any square roots in a "good-looking" expression or a "bad-looking" one.) √A+√B --------------------------- √A - √B 1st rule "ANY DIVISOR?" We are able to do a such math operation (by the nice way), but only if A is the divisor of B or B is the divisor of A or we have the HCF of A and B bigger than 1. So √15 - √8 above expression we can't simplify ("nicely"), because we dont have any divisor there and no HCF (bigger than 1) either. 2nd rule "DIVIDING RULE" If we found some divisor of A and B or their HCF, we can use this procedure √45 - √5 just divide 45:5 = 9 then √9*√5 - √5 = 3√5 - √5 = 2√5 This is our "good looking" expression. The bad-looking expression (but, of course, we don't use that way, however, sometimes it could be usefull): √30 - √5 -----------------------> 30:5 = 6 √6*√5 - √5 = √5 (√6 - 1) If we have the case like that √18 - √8 we must use the HCF -----> HCF = 2 18:2 = 9 -------------------> 8:2= 4 √9*√2 - √4*√2 = √2 (3-2) = √2 The case with a "bad-looking" expression (but, of course, we don't use that way, however, sometimes it could be usefull): √15 - √6 we can use the HCF -----> HCF = 3 15:3 = 5 -------------------> 6:2 = 3 √5*√3 - √3*√2 = √3 (√5 - √2)
I solved it in my head but a little bit different, I’m not sure if I just got lucky though. I multiplied (sqrt20 - sqrt5) by sqrt5 and got sqrt100 - sqrt25 and they simplify to 10-5 which led me to pick c Edit: I did the same thing for the last problem but multiplied sqrt18 - sqrt8 by sqrt2 and got sqrt36 - sqrt16 which simplifies to 6-4 which is 2, so option D
my thought process: root 25 is 5 so root 20 will probably be 4.something root 5 is probably about 2.5 4.something-2.5 is likely around 2.5 the only one that's around 2.5 is root 5
While actually knowing how to multiply/factor roots is easier, the multiple choice question does not require that. Root20 is between 4 and 5, say around 4.5 (20 being between 16 and 25). Root5 is 2 and change (5 being slightly bigger than 4 but significantly less than 9). So 4.5 minus 2 and change is going to be 2 and change. Root15 is going to be bigger than 3, throw that out. Root10 is also bigger than 3, throw that out. Root2.5 is less than 2, throw that out. Root5 is what's left.
A note for test takers: to save time, treat the radicals like units or variables. Usually the answer will be the one that is in the same "unit." In the original question, we know that radical 5 will be the unit, so the answer has the contain a radical 5. For the second question, once we reduce radical 18 and radical 8, we are left with "units" of radical 2. The only answer choice with the same "unit" is D.
The simplest method I came up with, to solve √20 - √5 = ? [√20 = 2√5(you can get it by factoring method)] (Since we can write 2√5 = √5 + √5) Now, √5 + √5 - √5 = √5 (cancelling or subtracting √5 - √5) So the answer is Option C) √5
I nailed that one in a matter of seconds, but the SAT isn't really hard, nor is the ACT, and they aren't supposed to be. They show objectively whether you learned anything in high school, and I love them for that. It doesn't matter if you brought something for every "teacher appreciation day".
i did a digit-by-digit estimate in binary and found sqrt(20) was exactly double sqrt(5). its pretty obvious there; since four is one of the factors of 20, it appeared in the binary representation with a pair of zeroes, which had the effect of shifting everything one bit leftward in the root, AKA multiplying by 2.
What I want to know is why he is holding a Poke' ball, with no reference to it at all. Is it his eraser? Maybe it it to catch new subs. "Gotta cetch 'em all!"
@@bprpmathbasics Ahhh, clever, but, is it a mic or a mic muff? I would put it on a mic stand or boom stand and tap it a couple of times with you pencil at the very beginning and say "Is this mic on?" even though you know it is. It's a common show-biz reference. Then you don't have a distracting element in your presentation.
I imagine that you can't draw too much attention to it or say "Gotta catch em all" or the like for trademark issues. ORRR you could say something like "Don't miss any of my lessons, gotta catch em all" and have that be part of your shtick. Consult your attorney on that one though. ;-)
At first i was like i have no clue but then i opened the video and when he said try it yourself i was instantly like ”yeah i remember how this is done” and got it right in a few seconds
I figured sqrt(20) is between sqrt(16) and sqrt(25), so let's say it is 4.5. Then sqrt(5) is between sqrt(4) and sqrt(9), but on the low end, so approximately 2.2. Then 4.5 - 2.2 is 2.3. Only sqrt(5) is close to that.
as we know: (a-b)*(a+b)=a^2 - b^2 so we have a-b, a+b = sqrt(20)+sqrt(5), a^2 - b^2 = 20 - 5 = 15 so to get a-b: 15 / (sqrt(20)+sqrt(5)) multiplying the upper and lower numbers in fraction on (sqrt(20)+sqrt(5)) we get (15*sqrt(20)+15*(sqrt(5)) / 20+20+5 15*sqrt(20)=30*sqrt(5) (30+15)*sqrt(5) / 45 sqrt(5) = a-b
Simplest method is this one (Indian Class 8 Basic method ) √20-√5 =√5×√4-√5 =√5(√4-1) [MULTIPLICATION IS DISTRIBUTIVE OVER ADDITION] =√5(2-1) [√4=2] =√5×1 =√5 EASIEST METHOD!!
oh damn, i really thought this was a trick question with me double guessing my answer of sqrt(5) because it was called a tricky SAT question. But it turns out that it was just a normal question.
Geometry can be used to solve this question √x can be seemed as the length of a square with area x. Since 5 is a quarter of 20, its length will be half of that of a square of area 20. So the other half must be of area 5 as well.
By drawing out the squares you can visualise that for √a + √b = √c, if a ≤ b, then 4a ≤ c ≤ 4b and 3a + b ≤ c. So for the second question, let c=18, then b = 8 (since c ≤ 4b), therefore a ≤ 10/3 ≈ 3.33. In the options, only option D satisfies the criteria.
4:20 Oh! I get it😲When you split the sqrt the sqrt of 20, you then do that to the sqrt of 4 BEFORE YOU DO ANYTHING ELSE. Then multiply that by ONE of the two sqrts of 5, and then subtract the OTHER one. Better remember that if I can get back into College Algebra.🙏🏻
This is a clever trick but you really need to remember all those square roots beforehand. An alternative way that applies to any numbers assigned in the square roots is to square the left side of the formula, and square root the result again.
Feel like ppl are over complicating this. This is a mc problem. What I immediately thought was root 20 is between 4-5. Root 5 is between 2-3. Which means that root 20 - root 5 is between 2-3. The only answer in between 2-3 there is c, root 5.
I just estimated since it's multiple choice; sqrt(16)=4 sqrt(25)=5 therefore sqrt(20)approximates 4.5 sqrt(4)=2 therefore sqrt(5)is a bit over 2 aproximately 4.5 minus a bit over 2 leaves only one reasonable choice
As someone jumping back into school after a 3 year break i enjoyed being able to pause and solve on my own!! I feel a little proud remembering how to do that one
The difficulty of the problem comes not from my own math abilities, but my own doubt in my math abilities. I legit got C in like three seconds, but I continued to second guess myself for minutes on end.
Can you solve 2^x=5^(x+2)?
Answer: ruclips.net/video/WL-npSEyVTo/видео.htmlsi=wYnDM4fJ3u9ROqRo
Thought Process:
sqrt(20) = sqrt(5 x 4)
sqrt(5 x 4) = 2sqrt(5)
2sqrt(5) - sqrt(5) = sqrt(5)
Yeah takes like 2 seconds hahah
And I thought I m doing some mistake since you can't get answer so easily
Same 👍
Thx
Easy
(√18)-(√8) is
(√9*√2)-(√4*√2) furthermore
3(√2)-2(√2)
Radicals are same so we can subtract it,right
So 3-2=1 Then,
1(√2) or simply (√2)
ruclips.net/video/cH0yvkYT1CU/видео.html
for me, i did
sqrt(18)-sqrt(8) is
(sqrt(9)*sqrt(2))-(sqrt(4)*sqrt(2)) that is
sqrt(2(sqrt(9)-sqrt(4))) that is
sqrt(2(3-2)) that is
sqrt(2*1) that is
sqrt(2)
@@7MinutozRapsLetrashey could you help me understand the step of
sqrt(2(sqrt(9)-sqrt(4)))
I don’t understand how you got there from
(sqrt(9)*sqrt(2)) - (sqrt(4)*sqrt(2))
@@marquis5178 im sorry this was almost a year ago and i dont remember my own maths 💀
Wait i remember
So, when you have, lets say sqrt(4)
You could do sqrt(2)*sqrt(2)=sqrt(2*2) = sqrt(4)
Basically, its sqrt(x*y) = sqrt(x)*sqrt(y)
@s5178The problem is partially due to a typo problem: when 7MRL typed _sqrt(2(sqrt(9)-sqrt(4)))_ they probably meant _sqrt(2)(sqrt(9)-sqrt(4))_ i.e. they got the shared factor _sqrt(2)_ out of the parentheses.
And because _sqrt(9)-sqrt(4)_ is 1, the equality's stayed correct, despite the typo braking down the reasoning.
Huh! It was easy, I solved it right away!!
me 2
Good. Have a gumdrop.
Dweeb
@@TheBatugan77 mad cuz he’s good at math? Enjoy hell
ikr this ain't tricky
@@TheBatugan77 bruh has never taken algebra lmfaoooo
Answer to hw question √2
1 + 1
√2 = 1,414...
@@florinpichiu691 *1.41
@@Baconindamorning You're right, but I personally prefer using three numbers after the comma, just to be more specific.
Because it's 3√2 - 2√2
You can also do it this way. If you notice that the radicands multiply to a perfect square, solve it algebraically by squaring both sides. So initially, the problem is sqrt(20) - sqrt(5) = x. When squaring both sides, you end up with sqrt(20)^2 - 2*sqrt(20*5) + (- sqrt(5))^2 = x^2. This yields 20 - 20 + 5 = x^2 or 5 = x^2. We know the solution is positive since sqrt(20) - sqrt(5) is positive, so we can ignore the negative solution to this quadratic, so the solution is x = sqrt(5).
Note that sqrt(144) is 12 or -12. I used 12, not sure how to justify throwing away -12, which would leave us with sqrt(50) = x.
Regarding the original problem, it is _not_ true that sqrt(20) - sqrt(5) is positive:
sqrt(20) - sqrt(5) = -4.47 - 2.236 = -6.7
@@daapdary while it is true that given x^2 = 20, x = +- 2*sqrt(5), the notation sqrt(x) assumes the positive result only. It's convention. That's why if you plug x = sqrt(20) into wolframalpha or sqrt(20) into calculator, it will only give the positive value.
@@theeternalsw0rd Good point, thanks! So, sqrt(144) is positive in my example, but if I had started with 144 and then took the square root, it would be ± sqrt(144). The convention makes sense: a square root _function_ (where the domain is nonnegative real numbers) might as well return the nonnegative square root.
That's exactly how I did it. Was about to comment but found yours...
This man explained it so well, but it didn't have to be so lengthy. This could've been done by prime factorization and grouping the factors into groups of two.
He did explain it well, especially for those who can’t remember the factors.
ruclips.net/video/syWx6dwWa-M/видео.html
@@bettygilliland456 Prime factors don't have to remembered in general, just the rules for divisibility for small primes (mainly 2, 3, and 5). Successively applying that (or doing a little more work for higher primes) gets you the factorization.
@@bettygilliland456You don't need to remember anything to factor 20. In fact if you can't factor 20 you should not be doing this problem.
Math is not about "know how to solve a problem". It's all about "find the solution yourself".
If you lack some critical skill that is needed for this level of problem, it's better to consolidate that first.
Hey yahtzee...
SHOVE your lengthy.
3√2 - 2√2 = √2
My approach:
Let the whole equation be x, and square both sides
then we have (sqrt(20) - sqrt(5))^2 = x^2
20 - 2 * sqrt(20) * sqrt(5) + 5 = x^2
20 - 2 * sqrt(20 * 5) + 5 = x^2
20 - 2*10 + 5 = x^2
5 = x^2
x = sqrt(5)
That's it
Why?
Just take sqrt of 5 out, 2-1=1 and get sqrt of 5.
@@Yesytsucks what?
@@diamondsky3787 root 20 equals 2 root5 so it is 2 root 5 - root5= root5
@@Yesytsucks everyone has different approach. Even i did it like him.
@@premnath2333 congratulations, you waisted a lot of time on a two step problem
This is a nice trick to know. Back in school I used to just put everything into a bracket and multiply it with itself so it would be something like (a-b)^2 which equals a^2 - 2ab +b^2 and then apply square root to this result; this way you get rid of the square root and ab would always give you a perfect square. If ab is not a perfect square this technique wouldnt work but neither would his.
Thought process:
2 is the square root of 4, so the square root of 5 is close to 2.
4 is the square root of 16 but since that is a bit further away from 20, changing the number to 4.5 is a bit over 20 so that works.
4.5 - 2 =2.5
Now since the answer asks for a square root, that number must be squared.
2.5 × 2.5 is around and closest to 5.
Final answer: square root 5.
That's what I thought at first as well but its not quite accurate I guess
Not that complicated , sqrt20 is the same thing as 2sqrt5 - sqrt5 answer is very simply and easily sqrt5
I thought in the same way as you.
solution by me : square root of 20 : 2 root 5. now 2root 5 - root5= root5(2-1) {taking root 5 as common} => root 5 x 1 = root 5.
2.5 x 2.5 is 6.25. Not really close to 5
sqrt(1.6)+sqrt(0.9) = ?
(A) 0.7 (B) 0.5 (C) 7sqrt(10)/10 (D) sqrt(10)/2
Answer here: ruclips.net/video/PWCx_dVs4xk/видео.html
For the tryout question, the answer is "D", square root of 2.
Square root of 18 is the same as 3 root 2, and square root of 8 is 2 root 2.
3 root 2 - 2 root 2 gives you root 2.
Nice video! I wonder how you came up the option of sqrt(2.5) 🤔
This is the kind of problem that seems tricky when you first glance at it, but is trivial when you think about it for a few seconds. It is ironic how things can be that way, that what you think is tricky is really simple, or conversely, what you think is simple is really quite tricky.
@UCxNMlPEiqKVeZZ6I8q_nJww There are some high-school students where I would be relieved if they could find the state that Chicago is in, on a map of the U.S., or tell you what year that the War of 1812 took place. So am joyful if they can solve this little math problem easily, which I am sure some can, and by rights, most of them should be able
@@tom-kz9pb When I first read that, I was doubted you. Then I remembered my classmates.
Sqrt(18) - Sqrt(8)
(Multiply everything by root 2)
=> {Sqrt(36) - Sqrt(16)}/(Sqrt(2)
= (6-4)/Sqrt(2)
= 2/Sqrt(2)
=> Sqrt(2)
This method is satisfying
thought process:
A = sqrt(20) - sqrt(5)
A^2 = (sqrt(20) - sqrt(5))^2
We can use a^2-2ab^-b^2
sqrt(20)^2 - 2 * sqrt(20 x 5) + sqrt(5)^2
20 - 2 * 10 + 5
A^2 = 5
sqrt(A^2)= sqrt(5)
mine seem to be different from others
abit excessive but it works
@@DylanKJW yea i wanted to be a little different lol
@seo-woojin lol that's what I did too i only know irrational equations so I did it like that
@@tzbq lol i forgot this vid one year ago 😂 seems i have gotten some likes and never knew
√18 - √8 = ?
(√9 • √2) - (√4 • √2)
3(√2) - 2(√2)
If ax - bx = (a-b)x
then answer is D, √2
omg i learned something im so proud
THANK YOU 🧠🙏🏻
The other way to do it without recalling the mathmatical relationhship of breaking out a square root under the radical is:
Simply estimate the square root of 20 which is between 4 and 5...let's call it 4.5.
Then do basic square root of 5 in your head and say that is ~ 2.2
Perform 4.5-2.2 = 2.2 or 2.3 and square it...again in your head = 5
So answer is square root of 5. This is made possible by multiple choice doing basic arithmetic in your head aka deduction.
Of course, the mathematical answer is pretty well known as well for people that passed math class and I have had a lot of calculus so not a big deal...lol.
Why is every SAT math question i see always so easy
As an Indian 9th grader this was not that tricky rather I think it's one of the places where i can easily score good marks
the biggest challenge with sat is the reading part
Damn that's relatable, solved it without breaking a sweat
You shouldn't be proud,in India we are doing much greater things than this in class 9
@@ts9dream in India do you do calculus I and II in 9th?
I agree
Another thought process
In this case, we can think with bounding the values.
Now that the perfect square roots are written down, you can evaluate that 4 < sqrt(20) < 5, and 2 < sqrt(5) < 3, so the answer is roughly 2, which in this case only corresponds with sqrt(5).
In tests like SAT, where you are given answers to choose from, and not specific values, this can be nice to use.
This can also help in general when you need to estimate the value of a square root, like sqrt(55) would be between 7 and 8.
Edit: for the bonus question, sqrt(18) is slightly above 4, and sqrt(8) is slightly below 3, so the answer would be slightly above 1, which in this case is ~1.4 = sqrt(2)
I just did a bunch of aproximations and got it wright from that
Edit to explain. I knew that square root of 20 would be a little under 4.5 (after checking work later its 4.472)
And i knew square root of 5 is under 2.5 but i knew it was more under 2.5 then the other number was under 4.5 so wighted it by making it 2.3. 4.5-2.3=2.2 thus logically square root of 5 was the closest.
I did it a little more complicated
Say / means Sqrt (easier to write)
/20 - /5 = x
(/20 - /5)² = x²
(/20)² + 2(/20 × -/5) + (/5)² = x²
20 + 2×-10 + 5 = x²
20 - 20 + 5= x²
5 = x²
/5 =x
Sqrt18-sqrt8
Sqrt (9*2) - sqrt (4*2)
3sqrt 2 - 2sqrt 2
Sqrt 2
Answer D
Calculated before seeing video and got it right...
My try before seeing: sqrt(20) can be written as sqrt(4) x sqrt(5)
So our expression now is
sqrt(5)*sqrt(4) - sqrt(5)
Factor out sqrt(5)
sqrt(5) ( sqrt(4) - 1)
sqrt(5) ( 2 - 1 )
sqrt(5) (1)
sqrt(5)
Hope am correct
same
Ye or I mean sqrt20 is just sqrt4 x sqrt5 which is just 2 sqrt5
2 sqrt5 - sqrt5 = sqrt5
You are correct but you took such a long route
@@finnwilde This was my thought too xD
sqrt(20) is something between 4 and 5, sqrt(5) is something between 2 and 3, so subtracting the two should give you something pretty close to 2.
sqrt(15) is almost 4, so that's out.
sqrt(10) is more than 3, so that's out.
sqrt(5) is between 2 and 3, so a possibility.
sqrt(2.5) is less than 2, so that's out.
Only the square root of 5 is in the expected ballpark, so that's gotta be it.
That's how I did it
@@katieevans6017 Me too! This approach had a nice *feel* to it.
Why wouldn’t you just do the problem? You can do it easily in your head. No guessing needed.
@@ES-hr6vg Because the idea of factoring the radicand doesn't always occur to some of us ;-) All the more so in a case like this where the numbers involved are all small enough that the closest perfect squares are trivial enough to do the estimations indicated.
@@sststr really? But factoring whatever you can wherever you can is generally best practice lol
Easiest questions i have seen in years 🙂
My method :-
We begin by taking the square of the expression.
(√20 - √5)^2
= 20 + 5 - 2 ( √100) [ By using the formula = ( a - b)^2 = a^2 + b^2 - 2ab
=20 +5 - 2(10)
=25-20
=5
= If, (√20 - √5)^2 = 5, then
= √20 - √5 = √5
I just did it by approximation. 4^2 and 5^2 are 16 and 25, so sqrt of 20 should be around 4.5, apply same logic to sqrt of 5 and you get around 2.2, so the answer is approx 2.3. srqt 5 seems closest to 2.3.
The multiple choice answers also make it way too obvious, since 15 and 10 are bigger than 3 squared and 2.5 is smaller than 2 squared. Sqrt of 5 is the only one that's even in the ballpark.
root(18) can be written as 3(root2) and root(8) can be written as 2(root2)
so it is 3(root2) - 2(root2) = root(2)
Just for fun:
Sqrt(20) - sqrt(5)
sqrt(5) * (sqrt(4) - 1)
-3 * sqrt(5)
4:26 (√2)
I looked at the thumbnail and solved it in less than a minute. It's really not that bad, it was easier for me cause I've been doing some review on this before school starts and may be more familiar with this at first glance. Otherwise, I don't see why it would seem like a hard SAT question.
Answer √2
Procedure:
√18 - √8
We brake down √18 = √2*√9
And √8 = √2*√4
√9 = 3
√4 = 2
So we have
18 = 3√2
8 = 2√2
3√2 - 2√2 = 1√2 = √2
Hope it’s clear.
E você está certo! A decisão certa é surpreendente!
Here's how I solved it:
√20 - √5
√5(√4 - √1)
√5(2 - 1)
√5(1)
= √5
You could've also taken the whole square as (a - b)² = a² - 2ab + b²
And the square rooted the answer
Using his method on the second equation, you can break down the sqrt(18) into sqrt(9)*sqrt(2) (you can also break it down into 3 and 6, but they aren't perfect squares, so they're not helpful) You can also break down the sqrt(8) into sqrt(4)*sqrt(2). Both 9 and 4 are perfect squares, so you end up with 3*sqrt(2)-2*sqrt(2). It becomes a simple case of 3-2=1, and you're left with sqrt(2), making the answer D.
Another method (more satisfying)
Multiply everything by square root 5
That gives - square root 100 - square root 25/ square root of 5
Which then gives - (10 - 5)/ sqrt(5)
=> 5/sqrt(5)
=> sqrt(5)
pretty nice
(SQRT 20 - SQRT 5) =
SQRT 5 × (SQRT 20 - SQRT 5) / SQRT 5 =
(SQRT 100 - SQRT 25) / SQRT 5 =
(10 - 5) / SQRT 5 =
5 / SQRT 5 =
(SQRT 5 / SQRT 5) × (5 / SQRT 5) =
(5 SQRT 5 / 5) =
SQRT 5
extremely over-the-top lol, takes too much time and opens up the possibility to make a mistake during the calculation
Wait wha- no way, a video from this guy that's actually easy
Hablo español, pero me gusta ver todo tipo de vídeos sin importar el idioma, porq entiendo los ejercicios a pesar de todo
ruclips.net/video/syWx6dwWa-M/видео.html
Wachate los videos en chino
We can see that sqrt(20) is between 4 and 5, and that 20 is 4 more than 16 but 5 less than 25, putting it at approximately 4+4/9, or 4.44.
And, we can see that sqrt(5) is between 2 and 3, and that 5 is 1 more than 4 but 4 less than 9, putting it at approximately 2+1/5, or 2.2.
If you want a formula for that, it's LB + (MT / (MT+LT)), where:
LB = The lower bound of possible values.
MT = The "more than" value, or how much more the parameter of the function is than the square of the lower bound.
LT = The "less than" value, or how much less the parameter of the function is than the square of the upper bound.
It's only an approximation, but it's more than enough to do a multiple choice question like this in your head.
In the case of sqrt(20), LB = 4, MT = 4, LT = 5, so we get 4+4/9.
In the case of sqrt(5), LB = 2, MT = 1, LT = 4, so we get 2+1/5.
Thus, sqrt(20) - sqrt(5) is approximately 4.44 - 2.2, or 2.24, which is incidentally the exact value of sqrt(5) to 2 decimal places, so it's pretty safe to say the answer is C.
EDIT: Oh, and applying this to the bonus question:
sqrt(18): LB = 4, MT = 2, LT = 7, so it is approximately 4+2/9, or 4.22
sqrt(8): LB = 2, MT = 4, LT = 1, so it is approximately 2+4/5, or 2.8
Thus, sqrt(18) - sqrt(8) is approximately 4.22 - 2.8, or 1.42, which I probably don't need to tell you is pretty darn close to sqrt(2), so the answer to that is D.
sqrt(20)
=sqrt(5 x 4)
=sqrt[5 x (2^2)]
=2sqrt(5)
2sqrt(5) - sqrt(5) = sqrt(5)
Literally takes like 5 seconds if you know your squareroots
same i thought
Can be done more easily by (a-b)² = x²
Where x is the answer
D as answer for the given question
Muito boa a aula!. Abraços professor.
I have a good and very simple method for my students.
If we want to add or subtract any two square roots, we need to use two rules.
(BTW, we can do that with any square roots in a "good-looking" expression or a "bad-looking" one.)
√A+√B --------------------------- √A - √B
1st rule
"ANY DIVISOR?"
We are able to do a such math operation (by the nice way), but only if
A is the divisor of B or B is the divisor of A or we have the HCF of A and B bigger than 1.
So
√15 - √8
above expression we can't simplify ("nicely"), because we dont have any divisor there and no HCF (bigger than 1) either.
2nd rule
"DIVIDING RULE"
If we found some divisor of A and B or their HCF, we can use this procedure
√45 - √5
just divide 45:5 = 9
then
√9*√5 - √5 = 3√5 - √5 = 2√5
This is our "good looking" expression.
The bad-looking expression (but, of course, we don't use that way, however, sometimes it could be usefull):
√30 - √5 -----------------------> 30:5 = 6
√6*√5 - √5 = √5 (√6 - 1)
If we have the case like that
√18 - √8
we must use the HCF -----> HCF = 2
18:2 = 9 -------------------> 8:2= 4
√9*√2 - √4*√2 = √2 (3-2) = √2
The case with a "bad-looking" expression (but, of course, we don't use that way, however, sometimes it could be usefull):
√15 - √6
we can use the HCF -----> HCF = 3
15:3 = 5 -------------------> 6:2 = 3
√5*√3 - √3*√2 = √3 (√5 - √2)
Все легко, просто приблизительно от корня 20 получаете 4, а от корня из 5 - 2. 4-2 = 2 и дальше уже выбираете самое близкое значение 😄
Ну, если в конце эту 2 возвести в корень, те √4 то да
Не знаю зачем возиться с приближениями, когда можно 30 секунд потратить и получить ответ как в видео
ruclips.net/video/syWx6dwWa-M/видео.html
ruclips.net/video/cH0yvkYT1CU/видео.html
I solved it in my head but a little bit different, I’m not sure if I just got lucky though.
I multiplied (sqrt20 - sqrt5) by sqrt5 and got sqrt100 - sqrt25 and they simplify to 10-5 which led me to pick c
Edit: I did the same thing for the last problem but multiplied sqrt18 - sqrt8 by sqrt2 and got sqrt36 - sqrt16 which simplifies to 6-4 which is 2, so option D
my thought process:
root 25 is 5 so root 20 will probably be 4.something
root 5 is probably about 2.5
4.something-2.5 is likely around 2.5
the only one that's around 2.5 is root 5
Are you an engineer by any chance?
ruclips.net/video/syWx6dwWa-M/видео.html
ruclips.net/video/cH0yvkYT1CU/видео.html
For u to subtract it, the number has to be the same under the square root right ?
While actually knowing how to multiply/factor roots is easier, the multiple choice question does not require that. Root20 is between 4 and 5, say around 4.5 (20 being between 16 and 25). Root5 is 2 and change (5 being slightly bigger than 4 but significantly less than 9). So 4.5 minus 2 and change is going to be 2 and change. Root15 is going to be bigger than 3, throw that out. Root10 is also bigger than 3, throw that out. Root2.5 is less than 2, throw that out. Root5 is what's left.
ruclips.net/video/syWx6dwWa-M/видео.html
sqrt(5), pull the 4 out as a 2 for the first and subtract like terms
Thought process
Sqrt 20- sqrt 5
= Sqrt 5 ( sqrt 4 - 1 )
= Sqrt 5 ( 2-1 )
= Sqrt 5 ( 1 )
= Sqrt 5
A note for test takers: to save time, treat the radicals like units or variables. Usually the answer will be the one that is in the same "unit." In the original question, we know that radical 5 will be the unit, so the answer has the contain a radical 5. For the second question, once we reduce radical 18 and radical 8, we are left with "units" of radical 2. The only answer choice with the same "unit" is D.
The simplest method I came up with, to solve √20 - √5 = ?
[√20 = 2√5(you can get it by factoring method)]
(Since we can write 2√5 = √5 + √5)
Now,
√5 + √5 - √5 = √5 (cancelling or subtracting √5 - √5)
So the answer is Option C) √5
you could also factor sqrt5 out of 2sqrt5-sqrt5
=sqrt5[2(1)-1]
=sqrt5(1)
=sqrt5
I nailed that one in a matter of seconds, but the SAT isn't really hard, nor is the ACT, and they aren't supposed to be. They show objectively whether you learned anything in high school, and I love them for that. It doesn't matter if you brought something for every "teacher appreciation day".
but GCSEs and A-levels tho in uk
i did a digit-by-digit estimate in binary and found sqrt(20) was exactly double sqrt(5). its pretty obvious there; since four is one of the factors of 20, it appeared in the binary representation with a pair of zeroes, which had the effect of shifting everything one bit leftward in the root, AKA multiplying by 2.
For the ending question
sqrt(18) - sqrt(8)
=sqrt(9) × sqrt(2) - sqrt(4) × sqrt(2)
=3 × sqrt(2) - 2 × sqrt(2)
=sqrt(2)
Love Algebra and Calculus (especially Green’s, and Stoke’s Taylor’s Theorem) and differential equations!
What I want to know is why he is holding a Poke' ball, with no reference to it at all. Is it his eraser? Maybe it it to catch new subs. "Gotta cetch 'em all!"
@@bprpmathbasics Ahhh, clever, but, is it a mic or a mic muff? I would put it on a mic stand or boom stand and tap it a couple of times with you pencil at the very beginning and say "Is this mic on?" even though you know it is. It's a common show-biz reference. Then you don't have a distracting element in your presentation.
I imagine that you can't draw too much attention to it or say "Gotta catch em all" or the like for trademark issues. ORRR you could say something like "Don't miss any of my lessons, gotta catch em all" and have that be part of your shtick. Consult your attorney on that one though. ;-)
I set sqrt(20) - sqrt(5) = x
On squaring both sides:
-> x^2 = 20 + 5 - 2 * sqrt(20) * sqrt (5)
-> x^2 = 25 - 2 * sqrt(100)
-> x^2 = 25 - 20 = 5
-> x = sqrt(5)
root 20 = 2 root 5
2 root 5 - root 5 = root 5
take sqrt20 - sqrt5 equal to x
take square on both sides solve for x sqr
then take square root on both sides
and answer is sqrt5
I just estimated
sqrt20 is 4.5 and sqrt5 is 2.
4.5 - 2 = 2.5
2.5 ^ 2 is roughly 5 therefore the answer must be C.
same
With those u can rlly go by aproximation and do it mentaly
sqrt(20) = ~4,5
sqrt(5) = ~2,3
4,5 - 2,3 = 2,2
2,2² = 4.84 = ~5
so its sqrt(5)
5min of video for 5 seconds of 5h grade math...
At first i was like i have no clue but then i opened the video and when he said try it yourself i was instantly like ”yeah i remember how this is done” and got it right in a few seconds
Better way, square the whole equation. That is 5. Then take root, that is √5
This also relies on the fact that you must make the expression contain roots of perfect squares only
@@ATeima-kk5ps kind of luck. But I works for sure
@@anirudh7455 no i didnt say the solution luckily worked for you, i just said that its not "better" than his solution. Still a good solution though
👍
@@ATeima-kk5ps I actually worked this way because I looked at the options and their square would be a whole number.
@@anirudh7455 yeah it is a nice solution
Take root 5 common, answer is root 5(root 4- root 1) = root 5(2-1) = root 5
I did solved this type of questions in 9th.
The answer of the hwk is √2 option {d}.
ruclips.net/video/syWx6dwWa-M/видео.html
If this is tricky, I should have taken the SAT in 7th grade.
*root20=2root5*
*2root5-root5=root5*
root5+root5=2root5-root20 (checking answer)
Saraha ma3andich zhar la f tssahib la f zwaj walit tangoul tawahad maynawad tawahda Matahmal.....
Idk if anyone else did it my way but it was pretty funny:
=> √20 - √5 = x
=> 2√5 - √5 = x
=> (Factor out √5), √5(2-1) = x
=> √5(1) = **√5 = x**
Btw guys if you're not in algebra yet the thought process won't be as difficult as this he's just explaining the main idea of the question
I figured sqrt(20) is between sqrt(16) and sqrt(25), so let's say it is 4.5. Then sqrt(5) is between sqrt(4) and sqrt(9), but on the low end, so approximately 2.2. Then 4.5 - 2.2 is 2.3. Only sqrt(5) is close to that.
The moment u realise that √20 is 2√5
You rub ur nose on wall
D. 2^(1÷2)
as we know: (a-b)*(a+b)=a^2 - b^2
so we have a-b, a+b = sqrt(20)+sqrt(5), a^2 - b^2 = 20 - 5 = 15
so to get a-b:
15 / (sqrt(20)+sqrt(5))
multiplying the upper and lower numbers in fraction on (sqrt(20)+sqrt(5))
we get (15*sqrt(20)+15*(sqrt(5)) / 20+20+5
15*sqrt(20)=30*sqrt(5)
(30+15)*sqrt(5) / 45
sqrt(5) = a-b
ruclips.net/video/syWx6dwWa-M/видео.html
I like your work very much. I've already counted a few. Keep it up.
A thumbs up from me for that...thank you
My thought process was to square both sides and use the A2 + B2 - 2AB formula which gives us 20 +5 - 20 which gives us 5 this root 5 ans
Square both sides? Huh
C) 2(5)½
Very easy solved in mind🙃
Simplest method is this one (Indian Class 8 Basic method )
√20-√5
=√5×√4-√5
=√5(√4-1) [MULTIPLICATION IS DISTRIBUTIVE OVER ADDITION]
=√5(2-1) [√4=2]
=√5×1
=√5
EASIEST METHOD!!
Absolutely...
oh damn, i really thought this was a trick question with me double guessing my answer of sqrt(5) because it was called a tricky SAT question. But it turns out that it was just a normal question.
Geometry can be used to solve this question
√x can be seemed as the length of a square with area x. Since 5 is a quarter of 20, its length will be half of that of a square of area 20. So the other half must be of area 5 as well.
By drawing out the squares you can visualise that for √a + √b = √c, if a ≤ b, then 4a ≤ c ≤ 4b and 3a + b ≤ c.
So for the second question, let c=18, then b = 8 (since c ≤ 4b), therefore a ≤ 10/3 ≈ 3.33. In the options, only option D satisfies the criteria.
Root 20 can be 5x4, taking 2 out as 4 is square of 2. So left is 2root5 - root5= Root 5. Ezy 1 step answer
4:20 Oh! I get it😲When you split the sqrt the sqrt of 20, you then do that to the sqrt of 4 BEFORE YOU DO ANYTHING ELSE. Then multiply that by ONE of the two sqrts of 5, and then subtract the OTHER one. Better remember that if I can get back into College Algebra.🙏🏻
Learned something new today, thank you!
This is a clever trick but you really need to remember all those square roots beforehand. An alternative way that applies to any numbers assigned in the square roots is to square the left side of the formula, and square root the result again.
ruclips.net/video/syWx6dwWa-M/видео.html
Feel like ppl are over complicating this. This is a mc problem. What I immediately thought was root 20 is between 4-5. Root 5 is between 2-3. Which means that root 20 - root 5 is between 2-3. The only answer in between 2-3 there is c, root 5.
ruclips.net/video/syWx6dwWa-M/видео.html
I just estimated since it's multiple choice;
sqrt(16)=4
sqrt(25)=5
therefore
sqrt(20)approximates 4.5
sqrt(4)=2
therefore
sqrt(5)is a bit over 2
aproximately 4.5 minus a bit over 2 leaves only one reasonable choice
at that point you might as well just use a calculator ._.
sqrt(18)-sqrt(8) = sqrt(2)
Good video
As someone jumping back into school after a 3 year break i enjoyed being able to pause and solve on my own!! I feel a little proud remembering how to do that one
D is the answer to hw question
Rt 18=3 rt2
And rt 8=2 rt2
So ans =3rt2 -2rt2 =rt2
4:27
Answer -> D
I calculated it in my mind
The difficulty of the problem comes not from my own math abilities, but my own doubt in my math abilities. I legit got C in like three seconds, but I continued to second guess myself for minutes on end.
Great explanation! :)
I went with. Root20 ~ 4.5. Root 5 ~ 2 and a bit.
Thus 4.5-2abd a bit = 2 and a bit = Root5
Sqrt18 - sqrt 8
=( sqrt9 x sqrt2) - sqrt8. Sqrt of 9 is 3 So
=3 x sqrt2 - sqrt8
=3 x sqrt2- sqrt4 x sqrt2
=3 x sqrt2 -2 x sqrt2
Answer to the hw question is D. The square root of 18 minus the square root of 8 equals the square root of 2