Basic Math Examples

$- 12 + \sqrt{- 45} \div 3$

Step 1

Rewrite the division as a fraction.

$- 12 + \frac{\sqrt{- 45}}{3}$

Step 2

Pull out imaginary unit $i$ .

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Step 2.1

Rewrite $- 45$ as $- 1 (45)$ .

$- 12 + \frac{\sqrt{- 1 (45)}}{3}$

Step 2.2

Rewrite $\sqrt{- 1 (45)}$ as $\sqrt{- 1} \cdot \sqrt{45}$ .

$- 12 + \frac{\sqrt{- 1} \cdot \sqrt{45}}{3}$

Step 2.3

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

$- 12 + \frac{i \cdot \sqrt{45}}{3}$

$- 12 + \frac{i \cdot \sqrt{45}}{3}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 3.1.1

Factor $9$ out of $45$ .

$- 12 + \frac{i \sqrt{9 (5)}}{3}$

Step 3.1.2

Rewrite $9$ as $3^{2}$ .

$- 12 + \frac{i \sqrt{3^{2} \cdot 5}}{3}$

$- 12 + \frac{i \sqrt{3^{2} \cdot 5}}{3}$

Step 3.2

Pull terms out from under the radical.

$- 12 + \frac{i \cdot 3 \sqrt{5}}{3}$

$- 12 + \frac{i \cdot 3 \sqrt{5}}{3}$

Step 4

Move $3$ to the left of $i$ .

$- 12 + \frac{3 i \sqrt{5}}{3}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Cancel the common factor.

$- 12 + \frac{3 i \sqrt{5}}{3}$

Step 5.2

Divide $i \sqrt{5}$ by $1$ .

$- 12 + i \sqrt{5}$

$- 12 + i \sqrt{5}$

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