Greetings. Mentally I have calculated that the answer is 13 times the square root of 10. We determine that as follows. First we find the square root of 90. The square root of 90 is the same as the square root of 9 times the square root of 10 equals 3 times the square root of 10. We then multiply 3 times the square root of 10 by 3 resulting in 9 times the square root of 10 and it follows that the second part of the expression would work out to 4 times the square root of 10. Finally, we add 9 times the square root of 10 to 4 times the square root of 10 to get 13 times the square root of 10.
My grandfather was an engineer and as I was growing up, he insisted that we learn our multiplication tables up to 25*25 and the square roots from 1 to 10. In algebra, you can get by with simplification, but in engineering you do need to take that extra step. He often complained about the young men he worked with who constantly had to pull out their slide rules to do these “simple”problems. (Yes, this was before calculators.) While I don’t remember all of that now, I do remember enough that I am helping neighbors who are struggling to help their children learn these simple math techniques. I am going to suggest that they check out your RUclips channel because your explanations are clear and easy to follow. Do you have simple lessons for quadratic equations and polynomials?
When I started my study Building Enginering in 1981 we had to buy a slide ruler but never used is because the calculator took over. In 1982 I bought a Casio hand held computer to program calculations in Basic and one year later we programmed in Pascal en Fortran on personal computers. Nice to have been part of these developments in such a short period. It was only when my 6 yo daughter had to learn multiplication tables I rediscovered the beauty of math. I tought her how to calculate/estimate without calculator. Two years ago she came home to learn integration and differentiation in one weekend and past her test the next Monday. In 2022 I retired, getting bored and now I am teaching calculus to high school students as volunteer. Love math !!!
That’s what I did, thinking there would be a multiple choice question. And 13 X sq root of 10 (which is around 3.3) is going to get you in that same ballpark. But when in real life will this equation ever be relevant?
Yay! I couldn't quite remember what to do once I stripped it down to having the square root of 10 in both parts, so I did a couple of dummy problems to make sure adding them up was the proper course. Trust your instincts ... then verify. :)
Can you please break down all of the different types of problems and their formulas into a cohesive plan. How many different areas are there in this type of Math ?
Rule one, of millions or billions: 1. Learn to count. 2. Addition and subtraction is collected counting and it's inverse. So learn the addition tables. 3. Multiplication and division is collected addition and its inverse. So learn the Multiplication tables. 4. Powers and roots is collected Multiplication and its inverse. So learn ... to understand them.... ... And one Rule about all the above: they cannot be mixed before their values are converted to be of the same kind.
But an imperfect square would lead to an irrartional number. So the order of operations doesn't apply if irrational numbers are part of the equation?@@enriqueiii9209
3X square root 90 + 2Xsquare root 40 = 3Xsr9Xsr10 + 2Xsr4xsr10 = 3x3Xsr10 + 2xsr2xsr10= 9Xsr10 + 4Xsr10 = 13Xsr10 Final answer Had to brush up on factoring. Final answer might be 13x3.16 = 41.08 but too tired to ponder. Just making stuff up now!
Here is a simple math challenge. Draw a circle of radius (√5+1)/2 and inscribe a regular decagon. What is the decagon's perimeter? Hint: The superscribing circle's circumference is (√5+1)π ≈ 10.2, so the decagon's perimeter will be a bit less than this. Of course this problem will be simple if you know the trick (there is always a trick in math challenge problems) otherwise you are free to cheat and use your pocket calculator and post an answer to 16 digit precision.
3 x sqrt 90 + 2 x sqrt 40 3 x (sqrt 9 x 10) + 2 x (sqrt 4 x 10) 3 x (sqrt 9 x sqrt 10) + 2 x (sqrt 4 x sqrt 10) 3 x 3 x (sqrt 10) + 2 x 2 x (sqrt 10) 9 x (sqrt 10) + 4 x (sqrt 10) 13 x sqrt 10 13(sqrt10)
Yeahhhhh! I really understood your lesson on this type of problems. Got the answer right before watching the explanation. Still frightening to see those ugly radicals at first but it could be worse. It could be geometry. :(
Why doesn’t 3 times radical (9*10) equal to 3 times radical 9 times 3 times radical 10, given that the original is 3 times the quantity (radical 9*10)? The same question for 2 times quantity (radical 4*10)?
That is how you treat addition problems. If you break into factors of a Multiplication similarly, you are putting more factors in. Here you would make the first part three times as big as it actually is.
I love your videos so much! My I make a suggestion? In today's over sensitive world I think your statement "MANY WILL GET THIS WRONG" should be changed to "LETS SEE WHO GETS THIS CORRECT?"..... haa.
Why do so many people feel compelled to repeat how they got the right answer, when the vid itself tells us how to get the correct answer? I get showing your work when you get it wrong, but these regurgitations by people- especially the ones who seem to believe that they're writing a text book on the subject - are bit much. I suspect these are the same people who go to music reax videos and believe their job as a viewer is to serve as a music historian for the creator, writing "Fun fact:" then giving them eight paragraphs on the dating history of Fleetwood Mac every time someone hears "Rhiannon" for the first time.
Your discussion about the plus minus values, when taking a root out is wrong. There is always both values, and they should not be ignored, for full understanding; I worked it out like this: 2 x sq.rt40 = 2 x sq.rt(4 x10) = 2 x ±2 × sq.rt.10 = 2 x 2 x ±1 x sq.rt.10 = 2 x 2 x sq.rt(1 × 10) = 4 × sq.rt.10 So, in words, when taking out only the positive value for the square root, this is possible only because we leave the ±result under the root sign, by not also taking the root of the ×1 part.
As a student with lots of gaps in my mathematical education I appreciate his breakdown of necessary math computation that for many more seasoned math students might seem like an over complicated explanation. As a child my dad would look at an equation 3x=12 and say x=4. If you know to divide each side as soon as 3x=12 appears you automatically know the answer is 4. 11 year old me did not know this so was super confused. This is an example of the mental computation that you gain as you do math that less experienced students get easily lost with if you don’t (painfully for you) break down each step. I actually loved being able to see inside the wheels turning at each steps.
what is 13times the square root of 10? The final answer is not here. Who cares if you have the equation at there end- what final answer does this come out to?
You can approximate the value of √(10) and then multiply the result by 13. Approximation from √(10): √(10) is near √(9) 10 - 9 = 1 √(9) = 3 3 + 1/(2 ‧ 3) = 3⅙ ≈ 3.17 Now you multiply 3.17 by 13. The Result is 41,08. Round: 41,1. The final answer is ≈41,1. Check with your calculator. Best regards Marcus 😎
I don't see how this is remotely difficult as it can be done mentally in less than 20sec as 13 x root 10. As long as you know the rules of exponents. You should perhaps explain something a bit more involved.
These are the mental game I frustrated with, I went to division right away you people would do that if so wrong way to teach someone they will get confused. I did. Not knowing how to do I multiple 3 × 90 plus 2 × 40 equivalent 350 square root having trouble braking down 350 square root but should be my answer
The roots are a higher order than multiplication and division, which are a higher order than plus minus. They cannot be jumbled and must be respectfully treated in terms of each other ... 3 x sq.rt. 90 is NOT 3 x 90. Before the three can in any form be multiplied by the 90, it must be expressed as a sq.rt. value ... 3 = sq.rt. 9. NOW you can multiply... Sq.rt.9 x sqrt 90 = Sqrt 810. Etc. But going in that direction makes the problem more complicated... easier to see that the values under the root symbols 90 and 40 are each an easy root x the root of ten. So take the 9 out as a three, and the 4 as a 2, and multiply with what is already outside the root sign; 3x3 and 2x2 each with the type of the root of ten. So you get 9 apples plus 4 apples = 13 apples, sorry, 13 roots of ten.
Sorry, but you do this ALL THE TIME. 2 x 2 is two multiplied by itself ONCE. So, 2 x 2 x 2, or two cubed, is two multiplied by itself TWICE. Logic. And counting. (If I’m wrong, then please show me. What, in your mind, is “two multiplied by itself once?” 2?)
Is any one else as irritated by this guy as I am with his 'many will get this wrong etc ' crap on all of his uploads. The guy should come with a maths health warning-as a successful ex teacher of maths over many years his jaundiced view of young peoples abilities appalls me!
Greetings. Mentally I have calculated that the answer is 13 times the square root of 10. We determine that as follows. First we find the square root of 90. The square root of 90 is the same as the square root of 9 times the square root of 10 equals 3 times the square root of 10. We then multiply 3 times the square root of 10 by 3 resulting in 9 times the square root of 10 and it follows that the second part of the expression would work out to 4 times the square root of 10. Finally, we add 9 times the square root of 10 to 4 times the square root of 10 to get 13 times the square root of 10.
Thank you for taking the time to explain all the steps to solve this problem. That's important to a lot of people.
My grandfather was an engineer and as I was growing up, he insisted that we learn our multiplication tables up to 25*25 and the square roots from 1 to 10. In algebra, you can get by with simplification, but in engineering you do need to take that extra step. He often complained about the young men he worked with who constantly had to pull out their slide rules to do these “simple”problems. (Yes, this was before calculators.)
While I don’t remember all of that now, I do remember enough that I am helping neighbors who are struggling to help their children learn these simple math techniques. I am going to suggest that they check out your RUclips channel because your explanations are clear and easy to follow. Do you have simple lessons for quadratic equations and polynomials?
When I started my study Building Enginering in 1981 we had to buy a slide ruler but never used is because the calculator took over. In 1982 I bought a Casio hand held computer to program calculations in Basic and one year later we programmed in Pascal en Fortran on personal computers. Nice to have been part of these developments in such a short period.
It was only when my 6 yo daughter had to learn multiplication tables I rediscovered the beauty of math. I tought her how to calculate/estimate without calculator. Two years ago she came home to learn integration and differentiation in one weekend and past her test the next Monday.
In 2022 I retired, getting bored and now I am teaching calculus to high school students as volunteer. Love math !!!
3 {9.5) + 2 {6.3} = 41.2 +/-
That’s what I did, thinking there would be a multiple choice question.
And 13 X sq root of 10 (which is around 3.3) is going to get you in that same ballpark.
But when in real life will this equation ever be relevant?
WOW!!! This time I actually amazed myself by getting this correct. Thanks.
Thanks prof, your lessons are most appreciated
Yay! I couldn't quite remember what to do once I stripped it down to having the square root of 10 in both parts, so I did a couple of dummy problems to make sure adding them up was the proper course. Trust your instincts ... then verify. :)
Thank You dear Mr Coker, Albuquerque High 60s for NOT taking us through this kind of mind boggling explanations on how to see and solve problems.
factoring was my weakness in Math....thanks
can be written as 9 X squareroot of 10 + 4 X Squareroot of 10 = 13 X square rootof 10 ( i can't write down the symbol of squareroot
Answer 41.109
I too did it with a calculator !
Can you please break down all of the different types of problems and their formulas into a cohesive plan. How many different areas are there in this type of Math ?
Math is a language. How many kinds of writing are there?
Rule one, of millions or billions:
1. Learn to count.
2. Addition and subtraction is collected counting and it's inverse. So learn the addition tables.
3. Multiplication and division is collected addition and its inverse. So learn the Multiplication tables.
4. Powers and roots is collected Multiplication and its inverse. So learn ... to understand them....
...
And one Rule about all the above: they cannot be mixed before their values are converted to be of the same kind.
Good video! Well explained.
Solution starts at 10:15
Don't you have to take the square roots before adding according to the order of operations? In other words take the square root of 10 first?
No cuz there's no square root for 10, 2 x 5.
But an imperfect square would lead to an irrartional number. So the order of operations doesn't apply if irrational numbers are part of the equation?@@enriqueiii9209
13×10^1/2
3X square root 90 + 2Xsquare root 40 =
3Xsr9Xsr10 + 2Xsr4xsr10 =
3x3Xsr10 + 2xsr2xsr10=
9Xsr10 + 4Xsr10 =
13Xsr10 Final answer
Had to brush up on factoring. Final answer might be 13x3.16 = 41.08 but too tired to ponder. Just making stuff up now!
Here is a simple math challenge. Draw a circle of radius (√5+1)/2 and inscribe a regular decagon. What is the decagon's perimeter? Hint: The superscribing circle's circumference is (√5+1)π ≈ 10.2, so the decagon's perimeter will be a bit less than this. Of course this problem will be simple if you know the trick (there is always a trick in math challenge problems) otherwise you are free to cheat and use your pocket calculator and post an answer to 16 digit precision.
13*sqrt(10)
13*(10)^1/2
41.08
Ans. 13✓10
3
3 x sqrt 90 + 2 x sqrt 40
3 x (sqrt 9 x 10) + 2 x (sqrt 4 x 10)
3 x (sqrt 9 x sqrt 10) + 2 x (sqrt 4 x sqrt 10)
3 x 3 x (sqrt 10) + 2 x 2 x (sqrt 10)
9 x (sqrt 10) + 4 x (sqrt 10)
13 x sqrt 10
13(sqrt10)
Yeahhhhh! I really understood your lesson on this type of problems.
Got the answer right before watching the explanation.
Still frightening to see those ugly radicals at first but it could be worse. It could be geometry. :(
3√90+2√40=9√10+4√10=
=13√10
13√10
Why doesn’t 3 times radical (9*10) equal to 3 times radical 9 times 3 times radical 10, given that the original is 3 times the quantity (radical 9*10)? The same question for 2 times quantity (radical 4*10)?
That is how you treat addition problems. If you break into factors of a Multiplication similarly, you are putting more factors in. Here you would make the first part three times as big as it actually is.
Answer is 42
13*sqrt(10)
I enjoy doing these because you always learn something new
13 X square root of 10.
I usually make a silly mistake like writing the question down wrong. I did do the question right that I actually wrote down.
My silly mistakes used to be things like 3 squared = 6 or 2×3 = 9. I know better, but sometimes it just comes out like that.🤨
Join the club. I reccon we all do that.
160
7 seconds, all in my head. What a trip, eh?!!!
41.1095; I used a calculator.
27500
I would have thought 3×SR(9×10) distributes to 3×SR9 × 3×SR10.
That's an easy mistake to make. I had to think twice why it wasn't true.
12?
I love your videos so much! My I make a suggestion? In today's over sensitive world I think your statement "MANY WILL GET THIS WRONG" should be changed to "LETS SEE WHO GETS THIS CORRECT?"..... haa.
I got 6%y-G², but I did have my oven set on delecates.
13 square root 10
Did this in my head; 13 -/(10). Fun stuff!
I was right but I thought I'd gone wrong because I was sure it was going to resolve to something rational.
I came up with 17 x sqrt 2 x sqrt 5.
Close enough for government work.
I got 13 root 10
I am 64, where were you when?
13 times the square root of 10
10 times the square root of 10
Why do so many people feel compelled to repeat how they got the right answer, when the vid itself tells us how to get the correct answer?
I get showing your work when you get it wrong, but these regurgitations by people- especially the ones who seem to believe that they're writing a text book on the subject - are bit much.
I suspect these are the same people who go to music reax videos and believe their job as a viewer is to serve as a music historian for the creator, writing "Fun fact:" then giving them eight paragraphs on the dating history of Fleetwood Mac every time someone hears "Rhiannon" for the first time.
Looks like 13*sqrt10
13 times the square root of 10.
Your discussion about the plus minus values, when taking a root out is wrong. There is always both values, and they should not be ignored, for full understanding; I worked it out like this:
2 x sq.rt40 =
2 x sq.rt(4 x10)
= 2 x ±2 × sq.rt.10
= 2 x 2 x ±1 x sq.rt.10
= 2 x 2 x sq.rt(1 × 10)
= 4 × sq.rt.10
So, in words, when taking out only the positive value for the square root, this is possible only because we leave the ±result under the root sign, by not also taking the root of the ×1 part.
In my opinion you make it more difficult than it is. When you know the basic rules, you can solve this easily.
As a student with lots of gaps in my mathematical education I appreciate his breakdown of necessary math computation that for many more seasoned math students might seem like an over complicated explanation. As a child my dad would look at an equation 3x=12 and say x=4. If you know to divide each side as soon as 3x=12 appears you automatically know the answer is 4. 11 year old me did not know this so was super confused. This is an example of the mental computation that you gain as you do math that less experienced students get easily lost with if you don’t (painfully for you) break down each step. I actually loved being able to see inside the wheels turning at each steps.
13√10. Solved in 3 seconds, and he talks about it for 17 minutes. 🤣🤣🤣
why isn't the answer +/- 13sqrt 10 and =/- 5 sqrt 10 ???
+/- 5 sqrt 10
27.500
11300
I'm falling asleep. Hurry up and get.... this thing ...... finished... ....Zzzzzzzzzz...
what is 13times the square root of 10? The final answer is not here. Who cares if you have the equation at there end- what final answer does this come out to?
Comes at as approximately 41.11 - leave it as it 13srt10, because the square root of 10 is irrational and so the more precise answer.
You can approximate the value of √(10) and then multiply the result by 13.
Approximation from √(10):
√(10) is near √(9)
10 - 9 = 1
√(9) = 3
3 + 1/(2 ‧ 3) = 3⅙ ≈ 3.17
Now you multiply 3.17 by 13. The Result is 41,08. Round: 41,1.
The final answer is ≈41,1.
Check with your calculator.
Best regards
Marcus 😎
I don't see how this is remotely difficult as it can be done mentally in less than 20sec as 13 x root 10. As long as you know the rules of exponents. You should perhaps explain something a bit more involved.
These are the mental game I frustrated with, I went to division right away you people would do that if so wrong way to teach someone they will get confused. I did. Not knowing how to do I multiple 3 × 90 plus 2 × 40 equivalent 350 square root having trouble braking down 350 square root but should be my answer
The roots are a higher order than multiplication and division, which are a higher order than plus minus. They cannot be jumbled and must be respectfully treated in terms of each other ... 3 x sq.rt. 90 is NOT 3 x 90.
Before the three can in any form be multiplied by the 90, it must be expressed as a sq.rt. value ... 3 = sq.rt. 9.
NOW you can multiply...
Sq.rt.9 x sqrt 90 =
Sqrt 810.
Etc.
But going in that direction makes the problem more complicated... easier to see that the values under the root symbols 90 and 40 are each an easy root x the root of ten. So take the 9 out as a three, and the 4 as a 2, and multiply with what is already outside the root sign; 3x3 and 2x2 each with the type of the root of ten. So you get 9 apples plus 4 apples = 13 apples,
sorry, 13 roots of ten.
Sorry, but you do this ALL THE TIME. 2 x 2 is two multiplied by itself ONCE. So, 2 x 2 x 2, or two cubed, is two multiplied by itself TWICE. Logic. And counting. (If I’m wrong, then please show me. What, in your mind, is “two multiplied by itself once?” 2?)
Calculator question. Anything else is wasting time.
Im completely lost. Off for a coffee and a valium. Good night from Australia 😴.
these are just silly puzzles for the sake of doing silly puzzles.
Mathematically absolutely and fully correct but so much empty talk!
13√10 in about10 seconds. Way, way too long. Sorry.
Apology not accepted
Is any one else as irritated by this guy as I am with his 'many will get this wrong etc ' crap on all of his uploads. The guy should come with a maths health warning-as a successful ex teacher of maths over many years his jaundiced view of young peoples abilities appalls me!
Sorry. I disagree at 14:53 minutes. I would factor out the SqRt[10].
--> 9•SqRt[10] + 4•SqRt[10]
--> SqRt[10] • (9 + 4)
--> 13•SqRt[10]
Your trouble is you talk too much about F'n nothings when you should really teach. And that is why many students are "put off maths".
I did this in my head and I got about 42 ish. Hopefully that's close enough for a pass