KEY CONCEPT: The √ notation tell us to take the POSITIVE square root of a value.
For example √25 = 5 and √49 = 7
Also recognize that √0 = 0

In general, we can say: If k ≥ 0, then √k ≥ 0

We have:
QUANTITY A: √(x²y²)
QUANTITY B: xy

QUANTITY A
We know that x² ≥ 0 for ALL values of x
And y² ≥ 0 for ALL values of y
So, x²y² ≥ 0
When we apply the above rule, we can conclude that √(x²y²) ≥ 0
In other words, √(x²y²) = some number that's greater than or equal to zero.

QUANTITY B
We're told that x is NEGATIVE, and that y is POSITIVE
So, xy = (NEGATIVE)(POSITIVE) = some NEGATIVE number.

We get:
QUANTITY A: some number that's greater than or equal to zero.
QUANTITY B: some NEGATIVE number.

Answer: A

Cheers,
Brent