Basic Math Examples

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

Step 1

Pull out imaginary unit

$i$ .

Tap for more steps...

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

$i$ .

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

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

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite

$24$ as

$2^{2} \cdot 6$ .

Tap for more steps...

Step 2.1.1

Factor

$4$ out of

$24$ .

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

Step 2.1.2

Rewrite

$4$ as

$2^{2}$ .

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

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

Step 2.2

Pull terms out from under the radical.

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

Step 2.3

Multiply

$2$ by

$- 1$ .

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

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

Step 3

Cancel the common factor of

$8 - 2 i \sqrt{6}$ and

$4$ .

Tap for more steps...

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.

Tap for more steps...

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.

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

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

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

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