Simplify 4 square root of 44x^6y^5

$4 \sqrt{44 x^{6} y^{5}}$

Step 1

Rewrite $44 x^{6} y^{5}$ as ${(2 x^{3} y^{2})}^{2} \cdot (11 y)$ .

Factor $4$ out of $44$ .

$4 \sqrt{4 (11) x^{6} y^{5}}$

Rewrite $4$ as $2^{2}$ .

$4 \sqrt{2^{2} \cdot 11 x^{6} y^{5}}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$4 \sqrt{2^{2} \cdot 11 {(x^{3})}^{2} y^{5}}$

Factor out $y^{4}$ .

$4 \sqrt{2^{2} \cdot 11 {(x^{3})}^{2} (y^{4} y)}$

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$4 \sqrt{2^{2} \cdot 11 {(x^{3})}^{2} ({(y^{2})}^{2} y)}$

Move $11$ .

$4 \sqrt{2^{2} {(x^{3})}^{2} {(y^{2})}^{2} \cdot 11 y}$

Rewrite $2^{2} {(x^{3})}^{2} {(y^{2})}^{2}$ as ${(2 x^{3} y^{2})}^{2}$ .

$4 \sqrt{{(2 x^{3} y^{2})}^{2} \cdot 11 y}$

Add parentheses.

$4 \sqrt{{(2 x^{3} y^{2})}^{2} \cdot (11 y)}$

Step 2

Pull terms out from under the radical.

$4 (2 x^{3} y^{2} \sqrt{11 y})$

Step 3

Multiply $2$ by $4$ .

$8 x^{3} y^{2} \sqrt{11 y}$