Simplify square root of -6* square root of -12

$\sqrt{- 6} \cdot \sqrt{- 12}$

Step 1

Rewrite $- 6$ as $- 1 (6)$ .

$\sqrt{- 1 (6)} \cdot \sqrt{- 12}$

Step 2

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$\sqrt{- 1} \cdot \sqrt{6} \cdot \sqrt{- 12}$

Step 3

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

$i \cdot \sqrt{6} \cdot \sqrt{- 12}$

Step 4

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

$i \cdot \sqrt{6} \cdot \sqrt{- 1 (12)}$

Step 5

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

$i \cdot \sqrt{6} \cdot (\sqrt{- 1} \cdot \sqrt{12})$

Step 6

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

$i \cdot \sqrt{6} \cdot (i \cdot \sqrt{12})$

Step 7

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

Factor $4$ out of $12$ .

$i \sqrt{6} \cdot (i \cdot \sqrt{4 (3)})$

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

$i \sqrt{6} \cdot (i \cdot \sqrt{2^{2} \cdot 3})$

Step 8

Pull terms out from under the radical.

$i \sqrt{6} \cdot (i \cdot (2 \sqrt{3}))$

Step 9

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

$i \sqrt{6} \cdot (2 \cdot i \sqrt{3})$

Step 10

Multiply $i \sqrt{6} (2 i \sqrt{3})$ .

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

$\sqrt{6} (2 (i^{1} i) \sqrt{3})$

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

$\sqrt{6} (2 (i^{1} i^{1}) \sqrt{3})$

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

$\sqrt{6} (2 i^{1 + 1} \sqrt{3})$

Add $1$ and $1$ .

$\sqrt{6} (2 i^{2} \sqrt{3})$

Combine using the product rule for radicals.

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

Multiply $6$ by $3$ .

$2 i^{2} \sqrt{18}$

Step 11

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

$2 \cdot - 1 \sqrt{18}$

Step 12

Multiply $2$ by $- 1$ .

$- 2 \sqrt{18}$

Step 13

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

Factor $9$ out of $18$ .

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

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

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

Step 14

Pull terms out from under the radical.

$- 2 (3 \sqrt{2})$

Step 15

Multiply $3$ by $- 2$ .

$- 6 \sqrt{2}$

Step 16

The result can be shown in multiple forms.

Exact Form:

$- 6 \sqrt{2}$

Decimal Form:

$- 8.48528137 \dots$

Simplify square root of -6* square root of -12

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