Chapter 0.9, Problem 18E

To determine

To simplify the given expression

Answer to Problem 18E

  $\frac{2}{5}\sqrt{\frac{6}{5}}$

Explanation of Solution

Given information:

  $\frac{\sqrt{24}}{\sqrt{125}}$

Calculation:

Simplifying,

  $\frac{\sqrt{2\times 2\times 2\times 3}}{\sqrt{5\times 5\times 5}}$

So,

  $\frac{2\sqrt{2\times 3}}{5\sqrt{5}}$

On solving,

  $\frac{2\sqrt{6}}{5\sqrt{5}}$

So,

  $\frac{2}{5}\sqrt{\frac{6}{5}}$