(The square root of 8 plus 1) divided by the square root of 8 =? Basic Algebra!
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- Опубликовано: 7 авг 2024
- How to simplify a square root fraction. Learn more math at TCMathAcademy.com/.
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![16 divided by [ (9 - 5) squared ] times 16 =? Can You Solve In Your Head?](http://i.ytimg.com/vi/MBlHXVxSuHA/mqdefault.jpg)
![16 divided by [ (9 – 5) squared ] times 16 =? Can You Solve In Your Head?](/img/tr.png)
It doesn't require an 18 minute explanation !
It does for those who don't understand it.
Especially for a problem which is solved in less than 18 seconds.
@@Nikioko Your statement isn't true for everyone.
Too much bla, bla, bla.
exactly. ridiculous wading through this.
Just use the time slider. You're not forced to listen to it.
Solved in 18 seconds, and he talks for 18 minutes.
@Nikioko Believe it or not, there really are people who can't solve this equation. I'm not one of them, but this is not proof they don't exist.
You made this more complicated than necessary. An equally valid answer is 1 + 1/2*sqrt (2) and you can get there in 3 steps
(Sqrt(8) +1)/sqrt (8) = sqrt (8)/sqrt(8) + 1/sqrt(8)
Simplifying you get
1 + 1/sqrt(8) = 1 + 1/2sqrt(2)
Agreed, too much talking about how to do it wrong & never gets to answer. Never spend time on the wrong way, Always refer & APPLY the basic properties (Assoc, Com, Dist, Eq & introduce vinculum). Here numerator tell us how many denominators are added. The rest is confusion. KISS - they will figure out the rest.
I can't agree with you. What he is doing is showing not how quickly or in the least amount of steps you can solve it but logic behind all this and widen the knowledge how to get to the solution. This may be useful in more complicated math problems.
I got 1 + sqrt(2)/4. I think perhaps something is wrong in your notation of the final simplified answer.
@@Gideon_Judges6 nope my simplification is correct. In fact they both are.
1/sqrt(8) = 1/sqrt(4*2) = 1/(2*sqrt(2)) = sqrt(2)/4
Multiply 1/2sqrt(2) by sqrt(2)/sqrt(2) and you get sqrt(2)/4
@@Gideon_Judges6 Yes, he did not go on to simplify all the way. But there is nothing wrong in his answer. It's just not finished completely. You are correct. If you take two more steps you get what you have written. I did, too.
Congratulations -- you made a simple process very complicated. ----> (4 + sqrt(2))/4
I can't agree with you. What he is doing is showing not how quickly or in the least amount of steps you can solve it but logic behind all this and widen the knowledge how to get to the solution. This may be useful in more complicated math problems.
@@user-ky5dy5hl4d Occam's razor. Best logic is the most efficient. Efficiency is important in mathematics, physics, and computer programming.
@@Dr_piFrog Correct. Logic is important in religions, too. Logic will lead to a conclusion that all religions are total BS.
no wonder so many people don't like math....if you need help falling asleep, this is a good vid to watch...
lol come take my math class you will be begging for this guy as a teacher.
How about 1 + (square root of 2 ) divided by 4 ???
If this is the correct answer, I would suggest the question should be: "Can you simplify to a common rational denominator?" I'm not sure how either the answer given or
1 + sqrt(2) / 4 "solves" the problem.
Well, it was (4 + √2)/4, but that is the simplest form. Not all simplifications give you something a LOT simpler. I think one point he was making here is that by convention, a radical should not be in the denominator. I don't really understand the reason for that (I've seen it in another video) but rules is rules, I guess.
Exactly. It's not a solution at all. Rationalising the denominator is not "simplifying" or "solving". Rationalising the denominator is just rationalising the denominator.
@@Astrobrant2(4+√2)/4 is no simpler than the original expression. Rationalising the denominator is not "simplifying" or "solving". Rationalising the denominator is just rationalising the denominator.
You say you don't really understand this convention of not having a radical in the denominator. That's probably because there is no good reason for such a convention. It's just needless dogma.
Indeed, in this very video he specifically uses a term that DOES have a radical in the denominator. He multiplies the entire thing by √8/√8, thereby demonstrating that radicals in denominators are not just OK, they can in fact be useful.
@@gavindeane3670u put me feelings into words. Thank you.
@@Astrobrant2 : The form with the "simpler" denominator would be easier to use if long division was the only method available for obtaining a decimal approximation.
Seems far simpler and clearer to just start with breaking the expression into the sum of 2 fractions
√8/√8 + 1/√8, which is (1 + 1/√8)
and then simplify to 1 + √2/4
I would have separated the numerator into two terms rationalizing the second term and left the answer as 1+ (sqrt(2)/4).
Wouldn't 1 + √(2)/4 be simpler? Seems weird to include the 4/4
I guess I don't understand how the "answer" is really any better than the "problem".
You want to get an integer plus or minus a fraction with whole number in the denominator to get a standard value.
@@kimobrien.You'll need to try that again. That didn't make any sense.
The person you replied to raised a completely valid point. The "answer" in this video is not a solution to or simplification of the original expression. It's just a different way of expressing the same thing.
@@gavindeane3670 You do this type of simplification in preparation for a decimal approximation. Doing the approximation of any root and dividing by a whole number is almost always much simpler than dividing a whole number by the decimal approximation or doing multiply decimal approximations and then multiplication or division. Also the smaller the number under the root sign the easier it is to calculate the approximation. It also provided a standard way to compare numbers like this. When I was in HS we didn't have hand held calculators either.
@@gavindeane3670 The correct answer is 1+√2/4
@@kimobrien. Rationalising the denominator is not simplifying. Rationalising the denominator is rationalising the denominator. It might be a useful thing to do sometimes, but he isn't presenting us with a particular requirement of some operation or calculation we need to do next. You are just assuming that the thing we need to do next is a thing that would be easier without a radical in the denominator. Even if that were true it's still not correct to describe the re-expression of (1+√8)/√8 as (4+√2)/4 or 1+√2/4 as "simplification". It's just expressing the same thing in a different way.
In the video he claims we are "solving" or "simplifying" the original expression. That's nonsense. All he needs to do is change the question to "Can you rationalise the denominator?". Then (4+√2)/4 and 1+√2/4 would be correct answers to that question. As the question is currently posed, (4+√2)/4 and 1+√2/4 cannot reasonably be described as "answers" at all.
Whilst it is true that (√8+1)/√8 is the same as (4+√2)/4, the idea that the first one is a question and the second one is the answer is just silly.
You can't have radicals in the denominator.
@@CAustin582 Of course you can have radicals in the denominator. It's perfectly fine. He uses a term with a radical in denominator in this very video. He multiplies the expression by √8/√8, thereby demonstrating that radicals in denominators are not just perfectly fine, they can also be useful.
Rationalising the denominator is not "solving" or "simplifying". Rationalising the denominator is rationalising the denominator. If he'd posed the question as "Can you rationalise the denominator?" then there would be no problem.
(√8+1)/√8 and (4+√2)/4 are just different but equally valid and correct ways of expressing the same value. This obsession he has with not permitting radicals in denominators is not mathematics. It's just needless dogma.
@@gavindeane3670 Of course it's fine to have radicals in the denominator in your steps or as part of the problem. The point is that it's not accepted as part of the solution.
@@CAustin582 It's not accepted as part of the solution BY THIS GUY. Mathematically it's perfectly acceptable and normal.
For example, the world is full of mathematicians and scientists and engineers who know that the sine and cosine of 45 degrees is 1/√2.
In this video he starts with an expression of the form (a+b)/c and he ends up with an expression of the form (a+b)/c. Regardless of what he says in the video, he has not in any way simplified the expression. It is exactly as simple as it was to start with. And "solve" is completely inappropriate for this.
@@gavindeane3670 Then you could also argue that 2/6 is just as valid of an answer as 1/3. Having a radical in the denominator doesn't break any rules of math; it's just a common convention for simplification. This guy definitely didn't make it up.
Could you make it any harder.
😂
Far too much talking
Do what I do, fast forward using the slider. The talking exists for those who need it.
Solve? Is it equation? I don't think so.
All you get is another formula. What is that in practical terms? Would it not be 1.353....?
Answer starts at 8:10
This can be simplified in five lines in less than 10 seconds.
There isn't a solution to an expression. You might simply it if clearly stated rules describing simplest forms are given first.
so, what is the answer ? (mine is 5/4sqrt2 )
...Which is (sqrt(8)+1)/sqrt(8), which evaluates to approximately 1.353553. Either form, or even 1+sqrt(2)/4, can be crunched to approximately 1.353553 equally as easily.
Multiply top and bottom by sqrt(8). Get 8 as the denominator (rationalize 🤓), multiply out the nominator to 8 + sqrt(8), and go from there. Not yet watched the vid, but I feel a bit more can be done. However, for the purpose of the exercise, I guess, the denominator, I’d give at least 80% credit at this stage 😎
Rewrite:
(8 ^ 1/2) / (8 ^ 1/2) + (1) / (8 ^ 1/2) .
The first set Cancels out Leaving 1 + (1/8 ^ 1/2)
We have a root in the denominator so we multiply the top and bottom by it:
1 + (1 * 8^ 1/2) divided by (8 ^ 1/2)²
1 + 2(2^1/2) / 8
The 1 is NOT affected by the denominator AND we can reduce the second part:
1 + (2^1/2) divided by 4
Technically the answer the professor gave is correct, BUT some (teachers like me) would mark that wrong because it wasn't FULLY reduced.
When you have a fraction as an exponent the numerator is a power and the denominator is the root. Also Remember the rule (x + y ) divided by (x) is the same as x divided by x + y divided by x. This is valid since both parts of the numerator are affected by the denominator.
Super simple and any of my passing 8th grade students would be able to solve this before going on Christmas break.
Simplify, not solve (in the title) please.
"Rationalise the denominator" not "simplify" (and yes, definitely not "solve").
Or if you separated the two terms, you could have 1+((1/4)sqrt(2)).
(4+ sqrt 2)/4 is not finished.
By partial fraction decomposition it becomes 1 + (1/(2* sqrt 2)).
Like this.
Sqrt 8= 2 * sqrt 2.
((2 * sqrt 2)+1)/(2* sqrt 2)
Decompose, the 2 sqrt 2's cancel,
Leaving (1 + (1/(2*sqrt 2))
When you say, "Can you solve?," that means, "What is the numerical value of this expression?" In this case, it is 1.3536. The question should be, "Can you reduce this expression?" For some reason, the presenter has an obsessive attachment to the idea that no expression should have a radical in the denominator. It's almost as bad as his near obsession with PEMDAS. In the Real World, where we want to see numbers, it makes absolutely no difference if there is a radical in the denominator or not.
🤓☝️
It's not even "Can you reduce this expression?". It's just "Can you rationalise the denominator?". That's literally all he's done.
The expression starts in the form (a+b)/c and by the end it's still in the form (a+b)/c.
Silver hammer. You are perfectly correct. Can you solve what?. You really hammered him. Good work.
John is just wasting our time. He should visit the John with sandpaper
@@harrymatabal8448 Rough crowd in here today...😁😲
I have to ask. What app are you using in this video?
Thank you. I home school my son, so I love to keep up with my Math Skills. I keep telling him that math in our language is known as " Mathafu" which deriveds from the word "Ma" meaning truth. This is commom in Bantu. It all comes from ancient Kemet, when the Atlantians, Tehuti and the rest of them arrived to teach the Kemites the truths and universal laws of the universe.
And your point is ?????
@@kingalfred3902 "Ma" what you call math is occult. If there is no limit to infinity ♾️ then zero is also an illusion. Tahiti said, "that which has a beginning has an end. And that which has no beginning has no end." We have totally misunderstood "zero" , that's why your calculator cannot divide by zero. Example: 1÷0 Once you understand this then, you are now knee deep in the unexplainable realm, which you call "Black Magic" or "The God Realm" where the laws of science do not apply.
1 + (1/sqrt(8))
=1+ sqrt(8)/8
oops
1 +(sqrt(8)/8)
No. It equals (8 + √8)/8. You forgot to multiply _both_ of the terms in the numerator by √8.
Also, you used the parentheses wrong in your first line. It should be (√8 + 1)/√8
Thank you. I was able to get the right answer.
YEA SURE ...!!!!.....
Yeah, me too, I just read down the comments to find the answer.
Thank you
What I'd like to know is how the answer is the problem simplified. All that work and still the answer is not simplified.
It's not any simpler, is it.
What he's actually done is rationalised the denominator, not simplified.
Here's an idea. How about getting right to solving (simplifying) the problem instead of showing us 5 ways how NOT to solve it? 95% of those who will take the time to watch the solution akready understand the concepts of identity and distribution, so it's not necessary to show us. For the few who don't , refer them to a separate tutorial about those things, and when they are good with that, THEN they can come back and apply those concepts to this problem. 90% of this video is a waste of time for 95% of the viewers.
I don't believe that this site is for people who want to proclaim their mathematical genius to the world, but instead is for dullards like me.
Is not a more elegant solution ...... 1+ 8 to the power -1/2 ?
This level and length of explanation is for a pupil who've just joined junior high school.
Perfect!
If I'm going in a shop to buy some tiles for my bathroom, the seller ask me "how many sqt do you need?" Obviously I'll answer 4+root os 2 divided by 4! It's super usefull and effective!
A really great explanation. I will take your Math Skills Rebuilder and your Pre Calculus courses just for the pleasure of learning.
super simple:
First step: reduce √8 + 1 to 2√2 + 1. Numerator is now 2√2 + 1
Second step: denominator is irrational due to the root sign so we rationalize it by multiplying the numerator and the denominator by √8
Numerator: (2√2 + 1) * √8 which is 2√16 + 2√2 which reduces further to 8 + 2√2.
Now the denominator: √8 * √8 is just 8.
Third Step reduce fraction further. 8, 2 , 8 can all be divided by 2 so factor out a 2 and we get the final answer of (4 +√2) / 4.
Because BOTH the 4 AND the √2 are divided by 4 we can NOT reduce this further.
Like I said super simple if you know what to do it should take no more than 30 seconds to do. (This was a step by step explanation so it makes it look like more work than it actually is)
1 + (sqrt(2)/4)
thanks for the fun.
Quanta enrolação para resolver um problema elementar. Fala sem parar
Thanks. Good video. I'm still smart at math even though I'm stupid at everything else in life.
I'll bet you're not!
@@nickfraser4599 muted
Seeing problems and methods like this makes me wonder how I ever made it through algebra. There must be some other way.
No one thinks the answer is 1. This was way more confusing than it needed to be.
break it down even further 1 + 1/4 x sqrt 2
The distributive property is taught in third grade. You made a simple problem very complicated.
Verdade
(√8+1)/√8 equals √8/√8+1/√8 equals 1+1/√8. Why is that not considered fully simplified?
1+(1/(2 sqrt 2))
Irrationals in the denominator are frowned upon, because they are way harder to calculate.
Also sqrt(8) can be simplified to 2sqrt(2).
So 1+1/sqrt(8)= 1+1/(2sqrt(2)) = 1+sqrt(2)/4
This guy is saying "simplify" when what he really means is "rationalise the denominator".
What he's doing here isn't simplification at all. His end point (and your end point) aren't any simpler than the starting point.
Good explanation for beginners. The truth is math often gets reduced to a series of tricks to squeeze out the answer. If you don't know the tricks it is difficult to intuitively find the answers. Yes, math people call them rules but essentially they are the tricks to solving equations. Students looking for a more straight forward process are often confused when confronted with these situations. Compounding the issue is there may be multiple ways of finding alternate forms of the answers. Often successful math skills come down to "training" the person to answer a problem in a certain way similar to Pavlov teaching his dogs. Not kind but often true.
So true. I am having problems with Algebra because it seems so arbitrary and impractical.
Gotcha!
What about 1 + (1/sqrt(8))?
Simplify sqrt 8 to 2 * sqrt 2
1+ 1/(2 sqrt 2)
That's also fine. You could express the √8 bit as 2√2 if you wanted to as well.
How is sq root of 8, 64? 8 squared is 64.
Isnt it ONE?
Multiply top and bottom by SR8 = (1 +SR8)/8. I failed to simplify it further by realizing that SR8 = 2*SR2
3/2
3 over 2
Basically 1 round up.
Oh man I got 1+sqrt2/4 I guess I better keep studying.
Your answer is better!!!
1.28868(approx.)
Can’t have the Square Root in the denominator and the answer is definitely not 1 May I suggest multiplying the top and the bottom by the SR of 8
Square roots in denominators are fine. They can even be useful - as you (and the video) demonstrate when you multiply this by √8/√8
I really don't know what you are saying. You give us an expression, not an equation and you ask us to solve it? What are you up to?
Why wouldn't you make it
1 + (√2/4)?
Doesn't the distributive property work in subtraction too?
(4+√2)/4 would become 4/4 + √2/4, which would reduce to 1 + √2/4.
You could look at it as distributing 1/4 times the components of the numerator.
You absolutely can express it as 1+√2/4. Nothing wrong with that at all.
It doesn't make sense to describe either 1+√2/4 or (4+√2)/4 as a "solution" to the original expression though. They're all just equivalent ways of saying the same thing.
I got that also. I broke the problem into 2 fractions which resulted in the 1 (like in your answer) with a denominator of 1 also. John's answer just combined both over a single denominator (4).
1.5 rounded to tenths
I feel for your class, How can a maths teacher waffle this much? Unbelievable!
1/rut 2
How about 1/4 * (4 + sum_(k=0)^∞ ((-1)^k (-1/2)_k (2 )^k )/(k!) ) No square root at all, just an infinite sum. Basic limits! Next challenge is to write it as an integral, no square root allowed.
1.472
Agree
(1 + ✓2)/ 4.
(√8 + 1) / √8
= (8 + √8) / 8
= 1 + 2√2 / 8
= 1 + √2 / 4.
Only when I have luxury of time then I would waste to watch his lectures and not to the fullest but skipping. However, if he cuts down unnecessarily talking and examples he would be the best of all.
One simple question, Given the number 4:
The square roots of 4 are +2 and -2. That needs to accounted for!
It's doesn't need to be accounted for. The √ symbol means "principal square root of", which is the positive square root.
Yes, 4 has two square roots, but √4 refers only to one of them. √4 is 2.
If you want to refer to both square roots you put ± in front of the √ symbol.
Solve??? No one can solve this because it is simply an expression, not something that can be solved such as an equation. Really shocking and disappointing that a math teacher doesn’t know the difference between solving and simplifying. Typical sloppy, irresponsible wording by someone who cares only about “likes” and “views” and has little or no interest in imparting knowledge.
Yeah, I noticed that, too. He's done it in other videos, as well. While the proper instruction would be "simplify", I can't really get bent out of shape over using the word, "solve". But then, you and I just see things differently, and that's okay.
@@Astrobrant2The proper instruction here wouldn't be "simplify". The proper instruction would be "rationalise the denominator".
@@gavindeane3670 Why tell them that? I mean, if the teacher wants to give them a clue, then okay, I won't object to that. But if rationalizing the denominator is something the students are expected to know and are being tested on, then "simplify" seems appropriate.
@@Astrobrant2Because rationalising the denominator is not simplifying. The "answer" in this video is not in any meaningful way a simplification of the original expression. They are just different ways of expressing the same thing.
If students are expected to be able to rationalise a denominator then that's fine. Test them on that. But ask them to do what you want them to do. If the requirement is to rationalise the denominator then the instruction should be "rationalise the denominator". It is absurd and inexcusable to obfuscate that requirement behind a different instruction that literally does not describe what you are asking them to do.
The square root of 16 is 4. The square root of 8 is @2.89. One-half of 8 is 4.
1+square root of 2 over 4
1.0607
(4+sqrt2)/4
Reduce further
1+1/(2√2)
Ans=√8/√8+1/√8=1+1/√8.
There is nothing to “solve “because there is no =. in math, language is important.
2 sqre root 8 +1
You can't solve this problem but you can simplify by rationalizing the denominator.
He's not solving it and he's not simplifying it either. He's just re-expressing the same thing in a different way.
Rationalising the denominator is not simplifying. Rationalising the denominator is rationalising the denominator.
Mathematicians are always “rationalizing” their beliefs. Lol😊
1+sqr root of 8
nearly 1.166
1+V2/4.
This is a joke right ?
😂
Good god. I saw the problem and thought “how can this equation be simplified down to a rational number?” 18 minutes I will never get back. I recommend you teach civics or something.
my first answer would be 1+1/sqrt(8)
Square root on 3
I tried, failed - will watch video now
It seems very long😂
1.o8
Congratulations, you simplified the original problem, but that doesn’t give us an actual answer. We would still need to use a calculator to find the value. Which we could have done in the first place without all of the simplification.
By the way the answer is 1.3535…
Ajab khan khattak.
Deviation...........deviation to
arrive at evaluation.
Solve or simplify? The genius at work again.
Neither. All he's doing is rationalising the denominator. He's not solving or simplifying anything.
@@gavindeane3670 You are another genius.
Huinya
4 steps,
Ans: 1 + (sqr(2))/4
wrong
@@bigdog3628It's not wrong. 1+(√2)/4 is equivalent to the original expression.
Find the comment section interesting. Very few understand the point of this channel. The point is to explain math in a way so even someone with zero mathing abilities will understand.
So many want to show off their minimal knowledge and say nonsense like, “I did this in minus 3 moves. That’s how good I am”. All sorts of pathetic. Just keep on keeping on.
Chat GPT4 got 1+√2/4
That's the same as what he gets in the video, just expressed in a slightly different way.
wow, it must be 1 + 1/sqrt8
it is said that maths skills in America are a scandal among the Earth's nations
bless this dude for attempting to rectify that
But in reality its probably a lost cause