Simplify (2 square root of 2x^2)(3x square root of x^2)

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

Step 1

Reorder $2$ and $x^{2}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Step 4

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

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

Step 5

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$2 (x^{1} x^{2}) \sqrt{2} \cdot 3$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 x^{1 + 2} \sqrt{2} \cdot 3$

Add $1$ and $2$ .

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

Step 6

Multiply $3$ by $2$ .

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