GMAT: square roots?

Question

I have noticed in my fumblings around the world of mathematics some funny things with square roots. For example:

(sqrt of 72) * pi = 6 * (sqrt of 2) * pi

I can see that something is happening here with factors of 72 but can't quite get my brain around what.

Pls advise. Many thanks.

Answer 1

That's because sqrt(72) can be simplified...

For instance... sqrt(72) = sqrt(8) * sqrt(9)

sqrt(8) = sqrt(4) * sqrt(2)

So... sqrt(72) = sqrt(4) * sqrt(2) * sqrt(9)

sqrt(4) = 2 and sqrt(9) = 3

Or sqrt(72) = 6 * sqrt(2)

The pi is just thrown on there to make it a little more complicated... :p

Answer 2

√72 = √(36*2) = √36 * √2
Now 36 is a square so your final answer is 6√2.

Answer 3

There would appear to be something missing, however π would indicate that this has something to do with a circle.

I have looked through the "mathcad" maths program handbook for this formula, but have drawn a blank.

Perhaps the questioner could expand a little

Answer 4

(sqrt of 72) * pi = 6 * (sqrt of 2) * pi
72^1/2 * pi = 6 * 2^1/2 * pi
6*2^1/2*pi = 6*2^1/2*pi
6 * (sqrt of 2) * pi = 6 * (sqrt of 2) * pi
Here what happens
72^1/2
72= 6^2 * 2 (both are equal)
(6^2 * 2)^1/2 (6 is squared then we can take out from sqrt)
6*(2)^1/2
6*sqrt(2)

Answer 5

72=36*2=6^2*2
therefore you can factor out 6 and get 6sqrt2=sqrt72

Answer 6

72 = 36 x 2
so sqrt of 72 = sqrt of 36 * sqrt of 2

sqrt of 36 = 6

that's how u get 6 x (sqrt of 2)

With some huge number under the square root, if the number ends with an even number such as 0, 2, 4, 6, 8, firstly divide it by 2, then 3, 5,7...ect.

So when you get a number that can square root by itself, the simplified number is your answer