Simplify square root of x^16y^35

$\sqrt{x^{16} y^{35}}$

Step 1

Rewrite $x^{16} y^{35}$ as ${(x^{8} y^{17})}^{2} y$ .

Rewrite $x^{16}$ as ${(x^{8})}^{2}$ .

$\sqrt{{(x^{8})}^{2} y^{35}}$

Factor out $y^{34}$ .

$\sqrt{{(x^{8})}^{2} (y^{34} y)}$

Rewrite $y^{34}$ as ${(y^{17})}^{2}$ .

$\sqrt{{(x^{8})}^{2} ({(y^{17})}^{2} y)}$

Rewrite ${(x^{8})}^{2} {(y^{17})}^{2}$ as ${(x^{8} y^{17})}^{2}$ .

$\sqrt{{(x^{8} y^{17})}^{2} y}$

Step 2

Pull terms out from under the radical.

$x^{8} y^{17} \sqrt{y}$