Simplify square root of x^18y^39

$\sqrt{x^{18} y^{39}}$

Step 1

Rewrite $x^{18} y^{39}$ as ${(x^{9} y^{19})}^{2} y$ .

Rewrite $x^{18}$ as ${(x^{9})}^{2}$ .

$\sqrt{{(x^{9})}^{2} y^{39}}$

Factor out $y^{38}$ .

$\sqrt{{(x^{9})}^{2} (y^{38} y)}$

Rewrite $y^{38}$ as ${(y^{19})}^{2}$ .

$\sqrt{{(x^{9})}^{2} ({(y^{19})}^{2} y)}$

Rewrite ${(x^{9})}^{2} {(y^{19})}^{2}$ as ${(x^{9} y^{19})}^{2}$ .

$\sqrt{{(x^{9} y^{19})}^{2} y}$

Step 2

Pull terms out from under the radical.

$x^{9} y^{19} \sqrt{y}$