Simplify 6y square root of 25x^3y^3

$6 y \sqrt{25 x^{3} y^{3}}$

Step 1

Rewrite $25 x^{3} y^{3}$ as ${(5 x y)}^{2} (x y)$ .

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

$6 y \sqrt{5^{2} x^{3} y^{3}}$

Factor out $x^{2}$ .

$6 y \sqrt{5^{2} (x^{2} x) y^{3}}$

Factor out $y^{2}$ .

$6 y \sqrt{5^{2} (x^{2} x) (y^{2} y)}$

Move $x$ .

$6 y \sqrt{5^{2} (x^{2}) y^{2} x y}$

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

$6 y \sqrt{{(5 x y)}^{2} x y}$

Add parentheses.

$6 y \sqrt{{(5 x y)}^{2} (x y)}$

Step 2

Pull terms out from under the radical.

$6 y (5 x y \sqrt{x y})$

Step 3

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

Move $y$ .

$6 (y \cdot y) (5 x \sqrt{x y})$

Multiply $y$ by $y$ .

$6 y^{2} (5 x \sqrt{x y})$

Step 4

Multiply $5$ by $6$ .

$30 y^{2} (x \sqrt{x y})$

Step 5

Reorder factors in $30 y^{2} (x \sqrt{x y})$ .

$30 y^{2} x \sqrt{x y}$