Question

Solve this please show your work <3

Answer 1

Given:

The expression is

$\sqrt[3]{48}=\sqrt[3]{8\cdot \_\_}=$

To find:

The simplified form of the expression.

Solution:

We have,

$\sqrt[3]{48}=\sqrt[3]{8\cdot \_\_}=$

The expression $\sqrt[3]{48}$ can be written as

$\sqrt[3]{48}=\sqrt[3]{8\cdot 6}$

$\sqrt[3]{48}=\sqrt[3]{8}\cdot \sqrt[3]{6}$       $[\because \sqrt[3]{ab}=\sqrt[3]{a}\sqrt[3]{b}]$

$\sqrt[3]{48}=2\cdot \sqrt[3]{6}$

$\sqrt[3]{48}=2\sqrt[3]{6}$

Therefore, $\sqrt[3]{48}=\sqrt[3]{8\cdot 6}=2\sqrt[3]{6}$.