Basic Math Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify each term.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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Step 2.4.1

Factor $4$ out of $12$ .

$- 2 - 3 (i \cdot \sqrt{4 (3)}) + 1 + 2 \sqrt{- 27}$

Step 2.4.2

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

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

Step 2.5

Pull terms out from under the radical.

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

Step 2.6

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

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

Step 2.7

Multiply $2$ by $- 3$ .

$- 2 - 6 (i \sqrt{3}) + 1 + 2 \sqrt{- 27}$

Step 2.8

Rewrite $- 27$ as $- 1 (27)$ .

$- 2 - 6 i \sqrt{3} + 1 + 2 \sqrt{- 1 (27)}$

Step 2.9

Rewrite $\sqrt{- 1 (27)}$ as $\sqrt{- 1} \cdot \sqrt{27}$ .

$- 2 - 6 i \sqrt{3} + 1 + 2 (\sqrt{- 1} \cdot \sqrt{27})$

Step 2.10

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

$- 2 - 6 i \sqrt{3} + 1 + 2 (i \cdot \sqrt{27})$

Step 2.11

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

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Step 2.11.1

Factor $9$ out of $27$ .

$- 2 - 6 i \sqrt{3} + 1 + 2 (i \cdot \sqrt{9 (3)})$

Step 2.11.2

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

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

Step 2.12

Pull terms out from under the radical.

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

Step 2.13

Move $3$ to the left of $i$ .

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

Step 2.14

Multiply $3$ by $2$ .

$- 2 - 6 i \sqrt{3} + 1 + 6 i \sqrt{3}$

Step 3

Simplify by adding terms.

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Step 3.1

Add $- 2$ and $1$ .

$- 6 i \sqrt{3} - 1 + 6 i \sqrt{3}$

Step 3.2

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

$0 - 1$

Step 3.3

Subtract $1$ from $0$ .

$- 1$