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GRE Quantitative Reasoning QUESTION #8114
Question 1

If $x > 0$ and $y > 0$, which of the following is equivalent to $\dfrac{x}{y}\sqrt{\dfrac{y}{x^2}}$?

  • $1$
  • $\dfrac{\sqrt{x}}{\sqrt{y}}$
  • $\sqrt{x}$
  • $\dfrac{1}{\sqrt{y}}$✔️
Correct Answer Explanation

Simplify step by step:

$\dfrac{x}{y} \cdot \sqrt{\dfrac{y}{x^2}} = \dfrac{x}{y} \cdot \dfrac{\sqrt{y}}{\sqrt{x^2}} = \dfrac{x}{y} \cdot \dfrac{\sqrt{y}}{x} = \dfrac{\sqrt{y}}{y} = \dfrac{1}{\sqrt{y}}$

The answer is $\dfrac{1}{\sqrt{y}}$.