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

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

Step 1

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

Factor $9$ out of $63$ .

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

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

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

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

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

Move $7$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

Move $y^{2}$ .

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

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

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

$2 (y^{2} y^{1}) (3 x \sqrt{7})$

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

$2 y^{2 + 1} (3 x \sqrt{7})$

Add $2$ and $1$ .

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

Step 4

Multiply $3$ by $2$ .

$6 y^{3} x \sqrt{7}$