Simplify 6 square root of 4x^2*2 square root of 9x^2y^2

$6 \sqrt{4 x^{2}} \cdot 2 \sqrt{9 x^{2} y^{2}}$

Step 1

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$6 \sqrt{{(2 x)}^{2}} \cdot (2 \sqrt{9 x^{2} y^{2}})$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$6 (2 x) \cdot (2 \sqrt{9 x^{2} y^{2}})$

Step 3

Multiply $2$ by $6$ .

$12 x \cdot (2 \sqrt{9 x^{2} y^{2}})$

Step 4

Rewrite $9 x^{2} y^{2}$ as ${(3 x y)}^{2}$ .

$12 x \cdot (2 \sqrt{{(3 x y)}^{2}})$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$12 x \cdot (2 (3 x y))$

Step 6

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

Move $x$ .

$12 (x \cdot x) \cdot (2 (3 y))$

Multiply $x$ by $x$ .

$12 x^{2} \cdot (2 (3 y))$

Step 7

Multiply $3$ by $2$ .

$12 x^{2} \cdot (6 y)$

Step 8

Rewrite using the commutative property of multiplication.

$12 \cdot 6 x^{2} y$

Step 9

Multiply $12$ by $6$ .

$72 x^{2} y$