Chapter 12.3, Problem 16E

To determine

To simplify: expression $-\sqrt{\frac{-25}{64}}$

Answer to Problem 16E

The required answer is: $\frac{5i}{8}$

Explanation of Solution

Given information:

The given expression: $-\sqrt{\frac{-25}{64}}$

Calculation:

  $-\sqrt{\frac{-25}{64}}=-\frac{\sqrt{-1\cdot 25}}{\sqrt{64}}$

(Product property of square roots)

  $\begin{array}{l}=-\frac{\sqrt{-1\cdot 5^2}}{\sqrt{8^2}}\\ =\frac{5i}{8}\end{array}$

(Simplify)

The square root of -1 is called an imaginary number and is represented by $i$