# Lesson: Operations with Roots

## Comment on Operations with Roots

### Sir in the related resources

Sir in the related resources in relation to this video, Do the Khan Academy has 700-800 level questions. I have Og 17, but i just want to practice more before looking at the official question. should i solve Khan Academy question (is it worth the time), or do i go to gmat club for practicing quant. The Khan Academy questions provided on the linked page are not 700+ questions. If 700+ level questions do exist on the GMAT, they are likely VERY RARE.

So, you might want to see what you can find on GMAT Club.

### I need some help with this

I need some help with this one: (root(9 + root(80)) + root(9 - root(80)))^2 = ### Thank you. Didn't see that

Thank you. Didn't see that the whole thing was being squared. I thought just the last expression was, so I was really confused.

### Hi Brent,

Hi Brent,

In the video you pointed out that if a root is divided, the number in front of the root is divided and the number inside the root is. But how is (9√5)/(3√15) = 3/√3 when 9/3 is 3 and 5/15 is not 3? ### You're correct about the rule

In general we can say:
(w√x)/(y√z) = (w/y)(√(x/z))

So, 9/3 = 3
And √5/√15 = √(5/15) = √(1/3)
So, we get: (9√5)/(3√15) = 3√(1/3) which is the same as 3/√3

At this point, we can simplify 3/√3 by multiplying top and bottom by √3.
We get: (3√3)/3 which equals √3

Does that help?

Cheers.
Brent