# 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

### Hey Brent, I see your

Hey Brent, I see your solution and it makes sense.

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

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

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

I'm wondering if there is a different approach?

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

I don't understand why isn't the answer B?

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

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

so if you square both side you get 21/36, which is 7/12, am i made a common mistake here...

### 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)