Simplify the Radical Expression square root of -3* square root of -12

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

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

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

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

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

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

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

Rewrite $- 12$ as $- 1 (12)$ .

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

Rewrite $\sqrt{- 1 (12)}$ as $\sqrt{- 1} \cdot \sqrt{12}$ .

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

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

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

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

Factor $4$ out of $12$ .

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

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

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

Pull terms out from under the radical.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Move $2$ to the left of $i$ .

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Rewrite $i^{2}$ as $- 1$ .

$2 \cdot - 1 {\sqrt{3}}^{2}$

Multiply $2$ by $- 1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$- 2 \cdot 3^{1}$

Evaluate the exponent.

$- 2 \cdot 3$

Multiply $- 2$ by $3$ .

$- 6$

Simplify the Radical Expression square root of -3* square root of -12

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