Simplify 2x^2y square root of 20x^4y^4

$2 x^{2} y \sqrt{20 x^{4} y^{4}}$

Rewrite $20 x^{4} y^{4}$ as ${(2 x^{2} y^{2})}^{2} \cdot 5$ .

Factor $4$ out of $20$ .

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

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

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

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

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

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

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

Move $5$ .

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

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

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

Pull terms out from under the radical.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

Move $y^{2}$ .

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

Multiply $y^{2}$ by $y$ .

Raise $y$ to the power of $1$ .

$2 x^{4} (y^{2} y^{1}) (2 \sqrt{5})$

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

$2 x^{4} y^{2 + 1} (2 \sqrt{5})$

Add $2$ and $1$ .

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

Multiply $2$ by $2$ .

$4 x^{4} y^{3} \sqrt{5}$