Which of the following expressions is equivalent to (sqrt(2q) + sqrt(r))^2/3, where q is greater....

Official May 2022 US SAT Section 3 Question 15:

Which of the following expressions is equivalent to (sqrt(2q) + sqrt(r))^2/3, where q is greater than 0 and r is less than 0 ?

[carter]

I think the question is different for you. This question on the SAT had a 2 as the coefficient for the r instead of it being by itself.

[페넬크리스토퍼]

If you figured this out, could you possibly revisit it? It's stumping my head over LOL (I searched it up and apparently D is the answer, but I'm not sure of how to obtain it)

[alialsaeed]

when i got to this question i just thought of a cube root and the stuff inside squared, when you square things like this they are gonna be in the form of (a^2+b^2+2ab) think about this thing and you'll get the answer immediately.
have a good day!!!

[zainababbasi]

the question you have does indeed contain a typo as there is a 2 with the r making it square root of 2r and not square root of r

[tas_]

it is raised to the power 2/3 which means cube root of (everything)^2
thats what raised to power 2/3 meant
and then you can use the (a+b)^2 formula which is a^2+ 2(a)(b) +b^2

[FalterwillIam]

Hi, I have solved the problem to (2qr)^1/6 (root 2q +root r+ 2)^1/3. If you can solve the problem from there it would be a great help. I can understand if you can't. : )