Chapter 12.3, Problem 15E

To determine

To simplify: expression $\sqrt{\frac{16}{-81}}$

Answer to Problem 15E

The required answer is: $\frac{4}{9i}$

Explanation of Solution

Given information:

The given expression: $\sqrt{\frac{16}{-81}}$

Calculation:

  $\sqrt{\frac{16}{-81}}=\frac{\sqrt{16}}{\sqrt{-1\cdot 81}}$

(Product property of square roots)

  $\begin{array}{l}=\frac{\sqrt{4^2}}{\sqrt{-1\cdot 9^2}}\\ =\frac{4}{9i}\end{array}$

(Simplify)

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