Chapter A.1, Problem 8E

Solution

Evaluate the expression without using a calculator.

  $4i$ .

Given:

The given expression is $\sqrt{-16}$ .

Concept Used:

• Root, in mathematics, a solution to an equation, usually expressed as a number or an algebraic formula.

Calculation:

The given expression is $\sqrt{-16}$ .

Square root of $\sqrt{-16}$ is:

Let $x=\sqrt[2]{-16}$

  $\begin{array}{l}x=\sqrt[2]{-16}\\ x=\sqrt[2]{4\cdot 4\cdot (-1)}\\ x=4\sqrt[2]{-1}\\ x=4i\end{array}$

Thus the solution of given expression $\sqrt{-16}$ is $4i$ .