Simplify 2y^2 square root of 8x^4y^4

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

Step 1

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

Factor $4$ out of $8$ .

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

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

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

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

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

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

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

Move $2$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 y^{2 + 2} (2 x^{2} \sqrt{2})$

Add $2$ and $2$ .

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

Step 4

Multiply $2$ by $2$ .

$4 y^{4} x^{2} \sqrt{2}$