Simplify (3 square root of 2x)(2 square root of 6x)

$(3 \sqrt{2 x}) (2 \sqrt{6 x})$

Step 1

Multiply $(3 \sqrt{2 x}) (2 \sqrt{6 x})$ .

Multiply $2$ by $3$ .

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

Combine using the product rule for radicals.

$6 \sqrt{6 x (2 x)}$

Multiply $2$ by $6$ .

$6 \sqrt{12 x \cdot x}$

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

$6 \sqrt{12 (x^{1} x)}$

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

$6 \sqrt{12 (x^{1} x^{1})}$

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

$6 \sqrt{12 x^{1 + 1}}$

Add $1$ and $1$ .

$6 \sqrt{12 x^{2}}$

Step 2

Rewrite $12 x^{2}$ as ${(2 x)}^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$6 \sqrt{4 (3) x^{2}}$

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

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

Move $3$ .

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

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

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

Step 3

Pull terms out from under the radical.

$6 (2 x \sqrt{3})$

Step 4

Multiply $2$ by $6$ .

$12 x \sqrt{3}$