Algebra Examples

\sqrt{- 12}

$\sqrt{- 12}$

Step 1

Rewrite

- 12

$- 12$ as

- 1 (12)

$- 1 (12)$ .

\sqrt{- 1 (12)}

$\sqrt{- 1 (12)}$

Step 2

Rewrite

\sqrt{- 1 (12)}

$\sqrt{- 1 (12)}$ as

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

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

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

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

Step 3

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

i \cdot \sqrt{12}

$i \cdot \sqrt{12}$

Step 4

Rewrite

12

$12$ as

2^{2} \cdot 3

$2^{2} \cdot 3$ .

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Step 4.1

Factor

4

$4$ out of

12

$12$ .

i \cdot \sqrt{4 (3)}

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

Step 4.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

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

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

Step 5

Pull terms out from under the radical.

i \cdot (2 \sqrt{3})

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

Step 6

Move

2

$2$ to the left of

i

$i$ .

2 i \sqrt{3}

$2 i \sqrt{3}$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$