Chapter 0, Problem 58PG

To determine

To simplify the expression $\sqrt{\frac{5}{81}}$

Answer to Problem 58PG

  $\frac{1}{9}\sqrt{5}$ is the simplified expression.

Explanation of Solution

Given information:

  $\sqrt{\frac{5}{81}}$

Calculation:

The given expression is $\sqrt{\frac{5}{81}}$

Simplifying,

  $\sqrt{\frac{5}{81}}=\sqrt{\frac{5}{9\times 9}}$

Taking out squares,

  $\sqrt{\frac{5}{81}}=\sqrt{\frac{5}{9^2}}$

So,

  $\sqrt{\frac{5}{81}}=\frac{1}{9}\sqrt{5}$

Hence, $\frac{1}{9}\sqrt{5}$ is the simplified expression.