Question

Simplify this radical. √x^13

Answer 1

x^(13/2) = x^(12/2)×sqrt(x)

x^6×sqrt(x) final answer

Answer 2

`\sqrt{x^(13)} = x^(6) * √(x)`.

Explanation:

Given :
`\sqrt{x^(13) }`.

To find : Simplify this radical.

Solution : We have given
`\sqrt{x^(13) }`.

By the exponent same base rule :
`x^(a) * x^(b) = x^(a +b)`.

Then we can write 13 as 12 + 1

`x^(12) * x^(1) = x^(12+1)`.

`x^(12) * x^(1) = x^(13)`.

`\sqrt{x^(13)} = \sqrt{x^(12)* x^(1) }`.

By the radical rule :
`\sqrt{x^(a)* x^(b) } = \sqrt{x^(a)} * \sqrt{x^(b)}`.

Then ,

`\sqrt{x^(13)} = \sqrt{x^(12)} * √(x)`.

`\sqrt{x^(13)} = x^{(12)/(2)} * √(x)`.

`\sqrt{x^(13)} = x^(6) * √(x)`.

Therefore,
`\sqrt{x^(13)} = x^(6) * √(x)`.