\(\sqrt{\frac{15}{2}}\) is the equivalent to sqrt(15) / sqrt (2).

1 squared = 1
2 squared = 3
3 squared = 9
4 squared = 16

We can use the above information to estimate the quantities in the equation.

sqrt(15) is a little less than 4
sqrt(2) is a little more than 1
3 = 3
sqrt(3) is a little less than 2

Roughly, then, the two quantities being compared are ~4 / ~1 and 3 / ~2. Even at this level of rounding, it's clear quantity A must be larger. Therefore, the correct answer choice is A.