Question

What is the simplest form of ^3 sqrt x^10

A: 3^3sqrtx

B: x^3sqrtx

C:x^3^3sqrtx

D:3c^3sqrtx

Answer 1

C on edge 2021

Explanation:

Answer 2

C.
`x^3\cdot \sqrt[3]{x}`

Explanation:

You are given the expression
`\sqrt[3]{x^(10)}`

Rewrite
`x^(10)` as
`x^3\cdot x^3\cdot x^3\cdot x`

Now

`\sqrt[3]{x^(10)}=\sqrt[3]{x^3\cdot x^3\cdot x^3\cdot x}`

For odd n, use the property of radicals

`\sqrt[n]{ab} =\sqrt[n]{a} \cdot\sqrt[n]{b}`

Hence

`\sqrt[3]{x^(10)}=\sqrt[3]{x^3\cdot x^3\cdot x^3\cdot x}=\sqrt[3]{x^3}\cdot \sqrt[3]{x^3}\cdot \sqrt[3]{x^3}\cdot \sqrt[3]{x}=x\cdot x\cdot x\cdot\sqrt[3]{x}=x^3\cdot \sqrt[3]{x}`