Question

Simplify:

a) $\sqrt[3]{-8}$

b) $\sqrt[4]{-81}$

c)$\sqrt[5]{-32}$

Short answer

a) $\sqrt[3]{-8}=-2$

b) $\sqrt[4]{-81}=NA$

c)$\sqrt[5]{-32}=-2$

Step-by-step solution

Part (a) Step 1: Given Information

The given expression is$\sqrt[3]{-8}$.

Part (a) Step 2: Simplification

As$-8={\left(-2\right)}^3$

Expression becomes $\sqrt[3]{{\left(-2\right)}^3}$

Simplifying gives$-2$

Part (b) Step 1: Given Information

The given expression is$\sqrt[4]{-81}$

Part (b) Step 2: Simplification

Fourth power of any number cannot be equal to a negative number.

Hence, no real number exists.

Part (c) Step 1: Given Information

The given expression is$\sqrt[5]{-32}$.

Part (c) Simplification

As ${\left(-2\right)}^5=-32$

Expression becomes $\sqrt[5]{{\left(-2\right)}^5}$

Simplifying gives$-2$