While solving GMAT quant questions, always remember that your __one__ goal is to identify the correct answer as efficiently as possible, and not to please your former math teachers.

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## Comment on

Operations with Roots## Sir in the related resources

## The Khan Academy questions

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

## Here's my step-by-step

Here's my step-by-step solution: https://gmatclub.com/forum/root-9-root-80-root-9-root-95570.html#p1891953

## Thank you. Didn't see that

## 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?

Thanks for the reply!

## You're correct about the rule

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

## Hey Brent, I see your

Algebraically, how would this look. I didn't see it the way you did and tried to mathematically solve it and kept getting 36. Maybe it's best I dont know lol but was curious as I was trying to take numbers out of the root sign

## What question are you

What question are you referring to?

## https://gmatclub.com/forum

Apologies!

## If you want to show your

If you want to show your solution, I can take a look.

## I'm wondering if there is a

https://gmatclub.com/forum/root-9-root-80-root-9-root-79493.html

## Question link: https:/

Question link: https://gmatclub.com/forum/root-9-root-80-root-9-root-79493.html

Aside from the strategies shown in the linked thread, the only other strategy I can think of is to use some estimation.

Estimation would help us eliminate 2 or 3 answer choices, but I think it would be pretty tricky to use straightforward rationale to justify why answer choice E (20) is a better estimate than answer choice D (18).

That said, on test day, if you're not sure what to do, estimation could help narrow your odds down to 50:50.

## I don't understand why isn't

https://gmatclub.com/forum/which-of-the-following-is-equivalent-to-242062.html

## Question link: https:/

Question link: https://gmatclub.com/forum/which-of-the-following-is-equivalent-to-24206...

I'm not sure how you would arrive at B, since it would be tricky to eliminate all roots.

Are you okay with the rationale for choice D?

## so if you square both side

## If there were an equation

If there were an equation here, we could square both sides.

So, let's create the equation: x = (√21)/6, which means our goal is to find the value of x.

If we square both sides we get: x² = 21/36

Simplify to get: x² = 7/12

Now take the square root of both sides: √(x²) = √(7/12)

Simplify: x = √(7/12)

Answer: D

## oh, i see what you meant,