Lesson: Operations with Roots

Comment on Operations with Roots

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.
gmat-admin's picture

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 one: (root(9 + root(80)) + root(9 - root(80)))^2 =

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,

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!
gmat-admin's picture

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?


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
gmat-admin's picture

What question are you referring to?


gmat-admin's picture

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

I'm wondering if there is a different approach?

gmat-admin's picture

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 the answer B?

gmat-admin's picture

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 you get 21/36, which is 7/12, am i made a common mistake here...
gmat-admin's picture

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, thanks now i getit

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