Simplify square root of 28x^3y^3

$\sqrt{28 x^{3} y^{3}}$

Step 1

Rewrite $28 x^{3} y^{3}$ as ${(2 x y)}^{2} \cdot (7 x y)$ .

Factor $4$ out of $28$ .

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

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

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

Factor out $x^{2}$ .

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

Factor out $y^{2}$ .

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

Move $x$ .

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

Move $7$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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