Simplify xy square root of 75x^2y^2

$x y \sqrt{75 x^{2} y^{2}}$

Rewrite $75 x^{2} y^{2}$ as ${(5 x y)}^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$x y \sqrt{25 (3) x^{2} y^{2}}$

Rewrite $25$ as $5^{2}$ .

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

Move $3$ .

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

Rewrite $5^{2} x^{2} y^{2}$ as ${(5 x y)}^{2}$ .

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

Pull terms out from under the radical.

$x y (5 x y \sqrt{3})$

Rewrite using the commutative property of multiplication.

$5 \sqrt{3} x y (x y)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$5 \sqrt{3} (x \cdot x) y \cdot y$

Multiply $x$ by $x$ .

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

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

$5 \sqrt{3} x^{2} y^{2}$