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## Comment on

Operations with Roots## For this problem:

a > 0

Quantity A: (4\sqrt{(5a)})^2

Quantity B: 40a

Quantity A:

[4√(5a)]² = [4√(5a)][4√(5a)]

= (16)(5a) ---> How do you get this? I would have thought 16 x sqrt(25a^2))

= 80a

## They're the same thing.

They're the same thing.

That is [4√(5a)]² = (16)[√(25a²)] = (16)[(√25)(√a²)] = (16)[(5)(a)] = 80a

## For the 2nd reinforcement

## Question link: https:/

Question link: https://greprepclub.com/forum/gre-math-challenge-91-a-697.html

Your approach is perfectly valid.

When we get to this point where we have...

QUANTITY A: 80a

QUANTITY B: 40a

...we could have just as easily divided both quantities by 80a (as you did) because we're told that a is positive.

When we do this, we get...

QUANTITY A: 1/2

QUANTITY B: 1

...in which case the answer is B.

Alternatively, we could have taken...

QUANTITY A: 80a

QUANTITY B: 40a

...and divided both quantities by 40a to get:

QUANTITY A: 2

QUANTITY B: 1

Answer: B

When it comes to applying the Matching Operations strategy (https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...), we'll always be okay as long as we follow a few basic rules about what can and can't be done.

Cheers,

Brent