We know that: \(x^2 = |y|\)

\(=> |x|^2 = |y|\)

\(=> |x| = \sqrt{|y|}\)

Thus, we need to compare:

Quantity A: \(|x| = \sqrt{|y|}\)
Quantity B: \(y\)

The various possibilities are:

#1. If \(y < 0\): Quantity A will be greater since it is positive while Quantity B is negative

#2. If \(y = 1\) or \(y = 0\): Quantity A will be equal to Quantity B, both being zero

#3. If \(0 < y < 1\): Quantity A will be greater than Quantity B since square root of a fraction is greater than the fraction itself (ex. \(\sqrt{0.49} = 0.7 > 0.49\))

#4. If \(y > 1\): Quantity B will be greater than Quantity A

Thus, there is no relation

Answer D