Simplify 8 square root of 8x^4y^6

$8 \sqrt{8 x^{4} y^{6}}$

Step 1

Rewrite $8 x^{4} y^{6}$ as ${(2 x^{2} y^{3})}^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$8 \sqrt{4 (2) x^{4} y^{6}}$

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

$8 \sqrt{2^{2} \cdot 2 x^{4} y^{6}}$

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

$8 \sqrt{2^{2} \cdot 2 {(x^{2})}^{2} y^{6}}$

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

$8 \sqrt{2^{2} \cdot 2 {(x^{2})}^{2} {(y^{3})}^{2}}$

Move $2$ .

$8 \sqrt{2^{2} {(x^{2})}^{2} {(y^{3})}^{2} \cdot 2}$

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

$8 \sqrt{{(2 x^{2} y^{3})}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$8 (2 x^{2} y^{3} \sqrt{2})$

Step 3

Multiply $2$ by $8$ .

$16 x^{2} y^{3} \sqrt{2}$