Chapter 12.3, Problem 8E

To determine

To simplify: expression $-\sqrt{-500}$

Answer to Problem 8E

The required answer is: $-10i\sqrt{5}$

Explanation of Solution

Given information:

The given expression: $-\sqrt{-500}$

Calculation:

  $-\sqrt{-500}=-\sqrt{-1\cdot 100\cdot 5}$

(Product property of square roots)

  $\begin{array}{l}=-\sqrt{-1\cdot {10}^2\cdot 5}\\ =-10i\sqrt{5}\end{array}$

(Simplify)

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