Simplify 5 square root of 2x*3 square root of 7x^2y^3

$5 \sqrt{2 x} \cdot 3 \sqrt{7 x^{2} y^{3}}$

Step 1

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

Factor out $y^{2}$ .

$5 \sqrt{2 x} \cdot (3 \sqrt{7 x^{2} (y^{2} y)})$

Move $7$ .

$5 \sqrt{2 x} \cdot (3 \sqrt{x^{2} y^{2} \cdot 7 y})$

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

$5 \sqrt{2 x} \cdot (3 \sqrt{{(x y)}^{2} \cdot 7 y})$

Add parentheses.

$5 \sqrt{2 x} \cdot (3 \sqrt{{(x y)}^{2} \cdot (7 y)})$

Step 2

Pull terms out from under the radical.

$5 \sqrt{2 x} \cdot (3 (x y \sqrt{7 y}))$

Step 3

Multiply $5 \sqrt{2 x} (3 x y \sqrt{7 y})$ .

Multiply $3$ by $5$ .

$15 \sqrt{2 x} (x y \sqrt{7 y})$

Combine using the product rule for radicals.

$15 (x y \sqrt{2 x (7 y)})$

Multiply $7$ by $2$ .

$15 (x y \sqrt{14 x y})$

$15 x y \sqrt{14 x y}$