Chapter 0.2, Problem 30E

To determine

The square root of $\sqrt{\frac{169}{196}}$ .

Answer to Problem 30E

The square root of $\sqrt{\frac{169}{196}}$ is $\frac{13}{14}$ .

Explanation of Solution

Given information:

The number $\sqrt{\frac{169}{196}}$ .

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 $\sqrt{\frac{169}{196}}$ .

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

Simplify $\sqrt{\frac{169}{196}}$ as,

  $\begin{array}{c}\sqrt{\frac{169}{196}}=\sqrt{\frac{13\times 13}{14\times 14}}\\ =\frac{13}{14}\end{array}$

Hence, the square root of $\sqrt{\frac{169}{196}}$ is $\frac{13}{14}$ .