Chapter A.1, Problem 12E

Solution

Evaluate the expression without using a calculator.

  $\frac{8}{5}$ .

Given:

The given expression is $\sqrt{\frac{64}{25}}$ .

Concept Used:

• Root, in mathematics, a solution to an equation, usually expressed as a number or an algebraic formula.

Calculation:

The given expression is $\sqrt{\frac{64}{25}}$ .

Square root of $\sqrt{\frac{64}{25}}$ is:

Let $x=\sqrt{\frac{64}{25}}$

  $\begin{array}{l}x=\sqrt[2]{\frac{64}{25}}\\ x=\sqrt[2]{\frac{(8)\cdot (8)}{5\cdot 5}}\\ x=\frac{8}{5}\end{array}$

Thus the solution of given expression $\sqrt{\frac{64}{25}}$ is $\frac{8}{5}$ .