Question

Simplify:

a) $\sqrt[3]{512}$

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

c)$\sqrt[5]{1}$

Short answer

a) $\sqrt[3]{512}=8$

b) $\sqrt[4]{81}=3$

c)$\sqrt[5]{1}=1$

Step-by-step solution

Part (a) Step 1: Given Information

The given expression is$\sqrt[3]{512}$

Part (a) Step 2: Simplification

As $512=8^3$

Expression becomes $\sqrt[3]{8^3}$

$=8$

Part (b) Step 1: Given Information

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

Part (b) Step 2: Simplification

As $81=3^4$

Expression becomes $\sqrt[4]{3^4}$

$=3$

Part (c) Step 1: Given Information

The given expression is$\sqrt[5]{1}$

Part (c) Step 2: Simplification

As $1=1^5$

Expression can be written as $\sqrt[5]{1^5}$

$=1$