Question

Simplify the radical, the square root of x^13

Answer 1

Rewrite it as a perfect square.

√x¹²x

Write it as a product of two radicals.

√x¹²√x

Simplify √x¹² (divide for 2)

√x¹² * 1/2

x⁶√x

Answer 2

√(x^13) is equal to:

(x^13)^(1/2)  which is equal to:

(x^12*x^1)^(1/2)  which is equal to

(x^12)^(1/2)*(x^1)^(1/2)

and the applicable rule:  (a^b)^c=a^(b*c) so

x^(12*1/2)*x^(1*1/2)

x^6*x^(1/2)

x^6√x