Question

What is the simplified version of 3\sqrt{135}

Answer 1

`9 √(15)`

Answer 2

The simplified version of
`\sqrt[3]{135}` is
`3\sqrt[3]{5}`.

Explanation:

The given expression is

`\sqrt[3]{135}`

According to the property of radical expression.

`\sqrt[n]{x}=(x)^{(1)/(n)}`

Using this property we get

`\sqrt[3]{135}=(135)^{(1)/(3)}`

`\sqrt[3]{135}=(27* 5)^{(1)/(3)}`

`\sqrt[3]{135}=(3^3* 5)^{(1)/(3)}`

`\sqrt[3]{135}=(3^3)^{(1)/(3)}* (5)^{(1)/(3)}`
`[\because (ab)^x=a^xb^x]`

`\sqrt[3]{135}=3* \sqrt[3]{5}`
`[\because \sqrt[n]{x}=(x)^{(1)/(n)}]`

`\sqrt[3]{135}=3\sqrt[3]{5}`

Therefore the simplified version of
`\sqrt[3]{135}` is
`3\sqrt[3]{5}`.