Algebra Examples

\sqrt{- 24}

$\sqrt{- 24}$

Step 1

Rewrite

- 24

$- 24$ as

- 1 (24)

$- 1 (24)$ .

\sqrt{- 1 (24)}

$\sqrt{- 1 (24)}$

Step 2

Rewrite

\sqrt{- 1 (24)}

$\sqrt{- 1 (24)}$ as

\sqrt{- 1} \cdot \sqrt{24}

$\sqrt{- 1} \cdot \sqrt{24}$ .

\sqrt{- 1} \cdot \sqrt{24}

$\sqrt{- 1} \cdot \sqrt{24}$

Step 3

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

i \cdot \sqrt{24}

$i \cdot \sqrt{24}$

Step 4

Rewrite

24

$24$ as

2^{2} \cdot 6

$2^{2} \cdot 6$ .

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Step 4.1

Factor

4

$4$ out of

24

$24$ .

i \cdot \sqrt{4 (6)}

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

Step 4.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

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

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

Step 5

Pull terms out from under the radical.

i \cdot (2 \sqrt{6})

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

Step 6

Move

2

$2$ to the left of

i

$i$ .

2 i \sqrt{6}

$2 i \sqrt{6}$

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

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