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

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

Step 1

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

Factor out $a^{2}$ .

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

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

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

Add parentheses.

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

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

Multiply $a$ by $a$ .

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

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

Step 6

Multiply $a^{2} \sqrt{3} \sqrt{2 a}$ .

Combine using the product rule for radicals.

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

Multiply $3$ by $2$ .

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

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

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