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}`.