Chapter 12.3, Problem 13E

To determine

To simplify: expression $\sqrt{18}\cdot \sqrt{-108}$

Answer to Problem 13E

The required answer is: $18i\sqrt{6}$

Explanation of Solution

Given information:

The given expression: $\sqrt{18}\cdot \sqrt{-108}$

Calculation:

  $\sqrt{18}\cdot \sqrt{-108}=\sqrt{9\cdot 2}\cdot \sqrt{-1\cdot 36\cdot 3}$

(Product property of square roots)

  $\begin{array}{l}=\sqrt{3^2\cdot 2}\cdot \sqrt{-1\cdot 6^2\cdot 3}\\ =3\sqrt{2}\cdot 6i\sqrt{3}\\ =18i\cdot \sqrt{2\cdot 3}\end{array}$

(Product property of square roots)

  $=18i\sqrt{6}$

(Simplify)

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