Simplify square root of x^12y^27

$\sqrt{x^{12} y^{27}}$

Step 1

Rewrite $x^{12} y^{27}$ as ${(x^{6} y^{13})}^{2} y$ .

Rewrite $x^{12}$ as ${(x^{6})}^{2}$ .

$\sqrt{{(x^{6})}^{2} y^{27}}$

Factor out $y^{26}$ .

$\sqrt{{(x^{6})}^{2} (y^{26} y)}$

Rewrite $y^{26}$ as ${(y^{13})}^{2}$ .

$\sqrt{{(x^{6})}^{2} ({(y^{13})}^{2} y)}$

Rewrite ${(x^{6})}^{2} {(y^{13})}^{2}$ as ${(x^{6} y^{13})}^{2}$ .

$\sqrt{{(x^{6} y^{13})}^{2} y}$

Step 2

Pull terms out from under the radical.

$x^{6} y^{13} \sqrt{y}$