Simplify square root of 12qr^2* square root of 3r

$\sqrt{12 q r^{2}} \cdot \sqrt{3 r}$

Step 1

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

Factor $4$ out of $12$ .

$\sqrt{4 (3) q r^{2}} \cdot \sqrt{3 r}$

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

$\sqrt{2^{2} \cdot 3 q r^{2}} \cdot \sqrt{3 r}$

Move $q$ .

$\sqrt{2^{2} \cdot 3 r^{2} q} \cdot \sqrt{3 r}$

Move $3$ .

$\sqrt{2^{2} r^{2} \cdot 3 q} \cdot \sqrt{3 r}$

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

$\sqrt{{(2 r)}^{2} \cdot 3 q} \cdot \sqrt{3 r}$

Add parentheses.

$\sqrt{{(2 r)}^{2} \cdot (3 q)} \cdot \sqrt{3 r}$

$\sqrt{{(2 r)}^{2} \cdot (3 q)} \cdot \sqrt{3 r}$

Step 2

Pull terms out from under the radical.

$2 r \sqrt{3 q} \cdot \sqrt{3 r}$

Step 3

Multiply $2 r \sqrt{3 q} \sqrt{3 r}$ .

Combine using the product rule for radicals.

$2 r \sqrt{3 r (3 q)}$

Multiply $3$ by $3$ .

$2 r \sqrt{9 r q}$

$2 r \sqrt{9 r q}$

Step 4

Rewrite $9 r q$ as $3^{2} (r q)$ .

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

$2 r \sqrt{3^{2} r q}$

Add parentheses.

$2 r \sqrt{3^{2} (r q)}$

$2 r \sqrt{3^{2} (r q)}$

Step 5

Pull terms out from under the radical.

$2 r (3 \sqrt{r q})$

Step 6

Multiply $3$ by $2$ .

$6 r \sqrt{r q}$

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