What is x^2y^2 if x 0?

Free Practice Question

PS · Problem Solving

555-605

Roots

What is $\sqrt{x^2y^2}$ if $x<0$ and $y>0$ ?

Answer Choices

Correct answer marked below

-xy

Correct

|x|y

-|xy|

|y|x

No solution

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Explanation

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Comments

LachlanApr 27

Thanks, this one tripped me up because I forgot to think about the signs. Good reminder to simplify inside the radical first.

SurenMay 9

Same here, the sign part is what makes it tricky.

AnshulMay 3

Yeah, always check the given conditions before jumping to the choices.

KarlApr 19

Quick question: after simplifying to |xy|, how do we decide which answer choice matches? I got stuck between two of them.

PrakharApr 25

Break |xy| into |x|·|y|, then use the signs given to rewrite |x| and |y|.

GerardoJul 7

Is the answer not just xy? I keep getting confused why the negative sign matters here.

SachinJul 9

Because x is negative, xy is negative, but the square root has to be nonnegative.

LeonardoJul 23

This felt right around 600 level. Straightforward if you know the rule, but the answer choices are designed to catch sign mistakes.

ChristopherJul 26

Agreed, the choices are the real trap here.

What this question tests

What it tests

Your handling of square and higher roots, including simplifying radicals.

Common trap

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.

What is x2y2\sqrt{x^2y^2}x2y2​ if x<0x<0x<0 and y>0y>0y>0?