Simplify the Radical Expression square root of 36xy^11

$\sqrt{36 x y^{11}}$

Step 1

Rewrite $36 x y^{11}$ as ${(6 y^{5})}^{2} (x y)$ .

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} x y^{11}}$

Factor out $y^{10}$ .

$\sqrt{6^{2} x (y^{10} y)}$

Rewrite $y^{10}$ as ${(y^{5})}^{2}$ .

$\sqrt{6^{2} x ({(y^{5})}^{2} y)}$

Move $x$ .

$\sqrt{6^{2} {(y^{5})}^{2} x y}$

Rewrite $6^{2} {(y^{5})}^{2}$ as ${(6 y^{5})}^{2}$ .

$\sqrt{{(6 y^{5})}^{2} x y}$

Add parentheses.

$\sqrt{{(6 y^{5})}^{2} (x y)}$

Step 2

Pull terms out from under the radical.

$| 6 y^{5} | \sqrt{x y}$

Step 3

Remove non-negative terms from the absolute value.

$6 | y^{5} | \sqrt{x y}$