Chapter A.1, Problem 9E

Solution

Evaluate the expression without using a calculator.

  $-6$ .

Given:

The given expression is $\sqrt[3]{-216}$ .

Concept Used:

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

Calculation:

The given expression is $\sqrt[3]{-216}$ .

Square root of $\sqrt[3]{-216}$ is:

Let $x=\sqrt[3]{-216}$

  $\begin{array}{l}x=\sqrt[3]{-216}\\ x=\sqrt[3]{(-6)\cdot (-6)\cdot (-6)}\\ x=-6\end{array}$

Thus the solution of given expression $\sqrt[3]{-216}$ is $-6$ .