Question

Simplify:

a) $\sqrt[3]{216}$

b) $\sqrt[4]{256}$

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

Short answer

a) $\sqrt[3]{216}=6$

b) $\sqrt[4]{256}=4$

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

Step-by-step solution

Part (a) Step 1: Given Information

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

Part (a) Step 2: Simplification

$216=6^3$

$\sqrt[3]{6^3}$

As $\sqrt[n]{a^n}=a$

$=6$

Part (b) Step 1: Given Information

The given expression is$\sqrt[4]{256}$

Part (b) Step 2: Simplification

As$256=4^4$

Expression becomes$\sqrt[4]{4^4}$

$=4$

Part (c) Step 1: Given Information

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

Part (c) Step 2: Simplification

As $32=2^5$

Expression becomes $\sqrt[5]{2^5}$

$=2$