Chapter 4.6, Problem 58SR

To determine

The simplified value.

Answer to Problem 58SR

The simplified value is $-120$ .

Explanation of Solution

Given:

  $4\sqrt{-9}\cdot 2\sqrt{-25}$

Calculation:

  $\begin{array}{c}4\sqrt{-9}\cdot 2\sqrt{-25}\\ =4\cdot 2\sqrt{-9}\cdot \sqrt{-25}\\ =8\cdot 3\cdot 5\sqrt{-1}\cdot \sqrt{-1}\left(\because i^2=-1\right)\\ =120\cdot i\cdot i\\ =120\cdot i^2\\ =120\left(-1\right)\\ =-120\end{array}$

Therefore,

The simplified value is $-120$ .