Basic Math Examples

$\frac{8 - \sqrt{- 24}}{4}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 24$ as $- 1 (24)$ .

$\frac{8 - \sqrt{- 1 (24)}}{4}$

Step 1.2

Rewrite $\sqrt{- 1 (24)}$ as $\sqrt{- 1} \cdot \sqrt{24}$ .

$\frac{8 - (\sqrt{- 1} \cdot \sqrt{24})}{4}$

Step 1.3

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

$\frac{8 - (i \cdot \sqrt{24})}{4}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $24$ as $2^{2} \cdot 6$ .

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Step 2.1.1

Factor $4$ out of $24$ .

$\frac{8 - i \cdot \sqrt{4 (6)}}{4}$

Step 2.1.2

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

$\frac{8 - i \cdot \sqrt{2^{2} \cdot 6}}{4}$

Step 2.2

Pull terms out from under the radical.

$\frac{8 - i \cdot (2 \sqrt{6})}{4}$

Step 2.3

Multiply $2$ by $- 1$ .

$\frac{8 - 2 i \sqrt{6}}{4}$

Step 3

Cancel the common factor of $8 - 2 i \sqrt{6}$ and $4$ .

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Step 3.1

Factor $2$ out of $8$ .

$\frac{2 (4) - 2 i \sqrt{6}}{4}$

Step 3.2

Factor $2$ out of $- 2 i \sqrt{6}$ .

$\frac{2 (4) + 2 (- i \sqrt{6})}{4}$

Step 3.3

Factor $2$ out of $2 (4) + 2 (- i \sqrt{6})$ .

$\frac{2 (4 - i \sqrt{6})}{4}$

Step 3.4

Cancel the common factors.

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Step 3.4.1

Factor $2$ out of $4$ .

$\frac{2 (4 - i \sqrt{6})}{2 \cdot 2}$

Step 3.4.2

Cancel the common factor.

$\frac{2 (4 - i \sqrt{6})}{2 \cdot 2}$

Step 3.4.3

Rewrite the expression.

$\frac{4 - i \sqrt{6}}{2}$