Simplify square root of 6a* square root of 3a^2

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

Step 1

Reorder $3$ and $a^{2}$ .

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

Step 2

Pull terms out from under the radical.

$\sqrt{6 a} \cdot (a \sqrt{3})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{3} \sqrt{6 a} a$

Step 4

Multiply $\sqrt{3} \sqrt{6 a}$ .

Combine using the product rule for radicals.

$\sqrt{3 (6 a)} a$

Multiply $3$ by $6$ .

$\sqrt{18 a} a$

Step 5

Rewrite $18 a$ as $3^{2} \cdot (2 a)$ .

Factor $9$ out of $18$ .

$\sqrt{9 (2) a} a$

Rewrite $9$ as $3^{2}$ .

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

Add parentheses.

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

Step 6

Pull terms out from under the radical.

$3 \sqrt{2 a} a$