Simplify this radical. √x^13

Question

asked Oct 8, 2019 96.8k views

2 Answers

Maccullt · Answer 1 · 2019-10-13T15:29:15+0000

Answer:

$\sqrt{x^(13)} = x^(6) * √(x)$ .

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,
$\sqrt{x^(13)} = x^(6) * √(x)$ .