Simplify y^2 square root of 63x^5y^4

$y^{2} \sqrt{63 x^{5} y^{4}}$

Rewrite $63 x^{5} y^{4}$ as ${(3 x^{2} y^{2})}^{2} \cdot (7 x)$ .

Factor $9$ out of $63$ .

$y^{2} \sqrt{9 (7) x^{5} y^{4}}$

Rewrite $9$ as $3^{2}$ .

$y^{2} \sqrt{3^{2} \cdot 7 x^{5} y^{4}}$

Factor out $x^{4}$ .

$y^{2} \sqrt{3^{2} \cdot 7 (x^{4} x) y^{4}}$

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

$y^{2} \sqrt{3^{2} \cdot 7 ({(x^{2})}^{2} x) y^{4}}$

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

$y^{2} \sqrt{3^{2} \cdot 7 ({(x^{2})}^{2} x) {(y^{2})}^{2}}$

Move $x$ .

$y^{2} \sqrt{3^{2} \cdot 7 ({(x^{2})}^{2}) {(y^{2})}^{2} x}$

Move $7$ .

$y^{2} \sqrt{(3^{2} ({(x^{2})}^{2})) {(y^{2})}^{2} \cdot 7 x}$

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

$y^{2} \sqrt{{(3 x^{2} y^{2})}^{2} \cdot 7 x}$

Add parentheses.

$y^{2} \sqrt{{(3 x^{2} y^{2})}^{2} \cdot (7 x)}$

Pull terms out from under the radical.

$y^{2} (3 x^{2} y^{2} \sqrt{7 x})$

Rewrite using the commutative property of multiplication.

$3 y^{2} (x^{2} y^{2} \sqrt{7 x})$

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

Move $y^{2}$ .

$3 (y^{2} y^{2}) (x^{2} \sqrt{7 x})$

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

$3 y^{2 + 2} (x^{2} \sqrt{7 x})$

Add $2$ and $2$ .

$3 y^{4} (x^{2} \sqrt{7 x})$

$3 y^{4} x^{2} \sqrt{7 x}$