Chapter 0, Problem 55PG

To determine

To simplify the expression $\sqrt{\frac{128}{5}}$

Answer to Problem 55PG

  $8\sqrt{\frac{2}{5}}$ is the simplified solution.

Explanation of Solution

Given information:

  $\sqrt{\frac{128}{5}}$

Calculation:

The expression is $\sqrt{\frac{128}{5}}$

Factorizing the expression,

  $\sqrt{\frac{128}{5}}=\sqrt{\frac{2\times 2\times 2\times 2\times 2\times 2\times 2}{5}}$

Taking pairs to square,

  $\sqrt{\frac{128}{5}}=\sqrt{\frac{{(2)}^2\times {(2)}^2\times {(2)}^2\times 2}{5}}$

Taking out square,

  $\sqrt{\frac{128}{5}}=2\times 2\times 2\sqrt{\frac{2}{5}}$

Hence, $8\sqrt{\frac{2}{5}}$ is the simplified solution.