Chapter 9.2, Problem 16E

To determine

The given expression in a simplified form

Answer to Problem 16E

$\frac{\sqrt{35}}{12}$

Explanation of Solution

Given:

The given expression is

$\sqrt{\frac{35}{144}}$

Calculation:

The expression can be simplified as

  $\begin{array}{l}=\sqrt{\frac{35}{144}}\\ =\frac{\sqrt{35}}{\sqrt{144}}\\ =\frac{{\left(35\right)}^{\frac{1}{2}}}{{\left(144\right)}^{\frac{1}{2}}}\\ =\frac{\sqrt{5\times 7}}{\sqrt{2\times 2\times 2\times 2\times 3\times 3}}\\ =\frac{\sqrt{5\times 7}}{\left(2\times 2\times 3\right)}\\ =\frac{\sqrt{35}}{12}\end{array}$