Basic Math Examples

$\frac{2 \sqrt{- 44}}{- 8}$

Step 1

Cancel the common factor of $2$ and $- 8$ .

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Step 1.1

Factor $2$ out of $2 \sqrt{- 44}$ .

$\frac{2 (\sqrt{- 44})}{- 8}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $- 8$ .

$\frac{2 \sqrt{- 44}}{2 \cdot - 4}$

Step 1.2.2

Cancel the common factor.

$\frac{2 \sqrt{- 44}}{2 \cdot - 4}$

Step 1.2.3

Rewrite the expression.

$\frac{\sqrt{- 44}}{- 4}$

$\frac{\sqrt{- 44}}{- 4}$

$\frac{\sqrt{- 44}}{- 4}$

Step 2

Pull out imaginary unit $i$ .

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Step 2.1

Rewrite $- 44$ as $- 1 (44)$ .

$\frac{\sqrt{- 1 (44)}}{- 4}$

Step 2.2

Rewrite $\sqrt{- 1 (44)}$ as $\sqrt{- 1} \cdot \sqrt{44}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{44}}{- 4}$

Step 2.3

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

$\frac{i \cdot \sqrt{44}}{- 4}$

$\frac{i \cdot \sqrt{44}}{- 4}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $44$ as $2^{2} \cdot 11$ .

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Step 3.1.1

Factor $4$ out of $44$ .

$\frac{i \sqrt{4 (11)}}{- 4}$

Step 3.1.2

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

$\frac{i \sqrt{2^{2} \cdot 11}}{- 4}$

$\frac{i \sqrt{2^{2} \cdot 11}}{- 4}$

Step 3.2

Pull terms out from under the radical.

$\frac{i \cdot 2 \sqrt{11}}{- 4}$

$\frac{i \cdot 2 \sqrt{11}}{- 4}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

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

$\frac{2 i \sqrt{11}}{- 4}$

Step 4.2

Cancel the common factor of $2$ and $- 4$ .

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Step 4.2.1

Factor $2$ out of $2 i \sqrt{11}$ .

$\frac{2 (i \sqrt{11})}{- 4}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $2$ out of $- 4$ .

$\frac{2 (i \sqrt{11})}{2 \cdot - 2}$

Step 4.2.2.2

Cancel the common factor.

$\frac{2 (i \sqrt{11})}{2 \cdot - 2}$

Step 4.2.2.3

Rewrite the expression.

$\frac{i \sqrt{11}}{- 2}$

$\frac{i \sqrt{11}}{- 2}$

$\frac{i \sqrt{11}}{- 2}$

Step 4.3

Move the negative in front of the fraction.

$- \frac{i \sqrt{11}}{2}$

$- \frac{i \sqrt{11}}{2}$

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