Chapter 0.2, Problem 29E

To determine

The square root of $\sqrt{\frac{16}{49}}$ .

Answer to Problem 29E

The square root of $\sqrt{\frac{16}{49}}$ is $\frac{4}{7}$ .

Explanation of Solution

Given information:

The number $\sqrt{\frac{16}{49}}$ .

Formula used:

The square root property which states that square root of any number can be expressed as,

  $\sqrt{\frac{{\text{a}}^2}{{\text{b}}^2}}=\frac{\text{a}}{\text{b}}$

Calculation:

Consider the given $\sqrt{\frac{16}{49}}$ .

Recall the square root property $\sqrt{\frac{{\text{a}}^2}{{\text{b}}^2}}=\frac{\text{a}}{\text{b}}$ .

Simplify $\sqrt{\frac{16}{49}}$ as,

  $\begin{array}{c}\sqrt{\frac{16}{49}}=\sqrt{\frac{4\times 4}{7\times 7}}\\ =\frac{4}{7}\end{array}$

Hence, the square root of $\sqrt{\frac{16}{49}}$ is $\frac{4}{7}$ .