Basic Math Examples

$2 \sqrt{- 3} - \sqrt{27} + 3 \sqrt{- 12}$

Step 1

Simplify each term.

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Step 1.1

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

$2 \sqrt{- 1 (3)} - \sqrt{27} + 3 \sqrt{- 12}$

Step 1.2

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

$2 (\sqrt{- 1} \cdot \sqrt{3}) - \sqrt{27} + 3 \sqrt{- 12}$

Step 1.3

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

$2 (i \cdot \sqrt{3}) - \sqrt{27} + 3 \sqrt{- 12}$

Step 1.4

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 1.4.1

Factor $9$ out of $27$ .

$2 i \sqrt{3} - \sqrt{9 (3)} + 3 \sqrt{- 12}$

Step 1.4.2

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

$2 i \sqrt{3} - \sqrt{3^{2} \cdot 3} + 3 \sqrt{- 12}$

Step 1.5

Pull terms out from under the radical.

$2 i \sqrt{3} - (3 \sqrt{3}) + 3 \sqrt{- 12}$

Step 1.6

Multiply $3$ by $- 1$ .

$2 i \sqrt{3} - 3 \sqrt{3} + 3 \sqrt{- 12}$

Step 1.7

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

$2 i \sqrt{3} - 3 \sqrt{3} + 3 \sqrt{- 1 (12)}$

Step 1.8

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

$2 i \sqrt{3} - 3 \sqrt{3} + 3 (\sqrt{- 1} \cdot \sqrt{12})$

Step 1.9

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

$2 i \sqrt{3} - 3 \sqrt{3} + 3 (i \cdot \sqrt{12})$

Step 1.10

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

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Step 1.10.1

Factor $4$ out of $12$ .

$2 i \sqrt{3} - 3 \sqrt{3} + 3 (i \cdot \sqrt{4 (3)})$

Step 1.10.2

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

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

Step 1.11

Pull terms out from under the radical.

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

Step 1.12

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

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

Step 1.13

Multiply $2$ by $3$ .

$2 i \sqrt{3} - 3 \sqrt{3} + 6 i \sqrt{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $2 i \sqrt{3}$ and $6 i \sqrt{3}$ .

$8 i \sqrt{3} - 3 \sqrt{3}$

Step 2.2

Reorder $8 i \sqrt{3}$ and $- 3 \sqrt{3}$ .

$- 3 \sqrt{3} + 8 i \sqrt{3}$