Question

What is the square root of ab2?

ab

a2b2
b2

Answer 1

There are two possible readings — I'll give both.

1) If the expression is a^2 b^2, then
sqrt(a^2 b^2) = sqrt(a^2) sqrt(b^2) = |a| |b| = |ab|.
(If a and b are known nonnegative, this equals ab.)

2) If the expression is a b^2, then
sqrt(a b^2) = sqrt(a) sqrt(b^2) = |b| sqrt(a).
(If b≥0 and a≥0 this is b√a.)

So for the multiple-choice options you listed, the correct choice for sqrt(a^2 b^2) is ab (more precisely |ab|).