Question

Rewrite in simplest radical form square root of x times the fourth root of x. Show each step of your process.

Answer 1

`√(x) \sqrt[4] x \\ \\ =\sqrt[4] {x^2} \sqrt[4]{x} \\ \\ =\boxed{\sqrt[4]{x^3}}`

Answer 2

`\sqrt[4]{x^3} = (\sqrt[4]{x})^3`

Explanation:

`√(x) * \sqrt[4]{x} =`

`= x^(1)/(2) * x^(1)/(4)`

`= x^{(1)/(2) + (1)/(4)}`

`= x^{(2)/(4) + (1)/(4)}`

`= x^(3)/(4)`

`= \sqrt[4]{x^3} = (\sqrt[4]{x})^3`