Simplify 7y^2 square root of 72x^2y^2

$7 y^{2} \sqrt{72 x^{2} y^{2}}$

Rewrite $72 x^{2} y^{2}$ as ${(6 x y)}^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$7 y^{2} \sqrt{36 (2) x^{2} y^{2}}$

Rewrite $36$ as $6^{2}$ .

$7 y^{2} \sqrt{6^{2} \cdot 2 x^{2} y^{2}}$

Move $2$ .

$7 y^{2} \sqrt{6^{2} x^{2} y^{2} \cdot 2}$

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

$7 y^{2} \sqrt{{(6 x y)}^{2} \cdot 2}$

Pull terms out from under the radical.

$7 y^{2} (6 x y \sqrt{2})$

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

Move $y$ .

$7 (y \cdot y^{2}) (6 x \sqrt{2})$

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

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

$7 (y^{1} y^{2}) (6 x \sqrt{2})$

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

$7 y^{1 + 2} (6 x \sqrt{2})$

Add $1$ and $2$ .

$7 y^{3} (6 x \sqrt{2})$

Multiply $6$ by $7$ .

$42 y^{3} x \sqrt{2}$