Simplify square root of 12* square root of -3

$\sqrt{12} \cdot \sqrt{- 3}$

Rewrite $- 3$ as $- 1 (3)$ .

$\sqrt{12} \cdot \sqrt{- 1 (3)}$

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$\sqrt{12} \cdot (\sqrt{- 1} \cdot \sqrt{3})$

Rewrite $\sqrt{- 1}$ as $i$ .

$\sqrt{12} \cdot (i \cdot \sqrt{3})$

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

Factor $4$ out of $12$ .

$\sqrt{4 (3)} \cdot (i \cdot \sqrt{3})$

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

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

Pull terms out from under the radical.

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

Multiply $2 \sqrt{3} (i \sqrt{3})$ .

Raise $\sqrt{3}$ to the power of $1$ .

$2 ({\sqrt{3}}^{1} \sqrt{3}) i$

Raise $\sqrt{3}$ to the power of $1$ .

$2 ({\sqrt{3}}^{1} {\sqrt{3}}^{1}) i$

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

$2 {\sqrt{3}}^{1 + 1} i$

Add $1$ and $1$ .

$2 {\sqrt{3}}^{2} i$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$2 {(3^{\frac{1}{2}})}^{2} i$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 \cdot 3^{\frac{1}{2} \cdot 2} i$

Combine $\frac{1}{2}$ and $2$ .

$2 \cdot 3^{\frac{2}{2}} i$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \cdot 3^{\frac{2}{2}} i$

Rewrite the expression.

$2 \cdot 3^{1} i$

Evaluate the exponent.

$2 \cdot 3 i$

Multiply $2$ by $3$ .

$6 i$