Question

Simplify this radical. √x^13

Answer 1

x^(13/2) = x^(12/2)×sqrt(x)

x^6×sqrt(x) final answer

Answer 2

Answer:

$\sqrt{x^{13}} = x^{6} * \sqrt{x}$.

Step-by-step 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  ,

$\sqrt{x^{13}} = \sqrt{x^{12}} * \sqrt{x}$.

$\sqrt{x^{13}} = x^{\frac{12}{2}} * \sqrt{x}$.

$\sqrt{x^{13}} = x^{6} * \sqrt{x}$.

Therefore, $\sqrt{x^{13}} = x^{6} * \sqrt{x}$.