Simplify (2 square root of 12a)(3 square root of 2a)

$(2 \sqrt{12 a}) (3 \sqrt{2 a})$

Step 1

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

Factor $4$ out of $12$ .

$2 \sqrt{4 (3) a} (3 \sqrt{2 a})$

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$2 (2 \sqrt{3 a}) (3 \sqrt{2 a})$

Step 3

Multiply $2$ by $2$ .

$4 \sqrt{3 a} (3 \sqrt{2 a})$

Step 4

Multiply $4 \sqrt{3 a} (3 \sqrt{2 a})$ .

Multiply $3$ by $4$ .

$12 \sqrt{3 a} \sqrt{2 a}$

Combine using the product rule for radicals.

$12 \sqrt{2 a (3 a)}$

Multiply $3$ by $2$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Step 5

Reorder $6$ and $a^{2}$ .

$12 \sqrt{a^{2} \cdot 6}$

Step 6

Pull terms out from under the radical.

$12 a \sqrt{6}$