Basic Math Examples

$\frac{- 30 + \sqrt{- 125}}{5}$

Step 1

Pull out imaginary unit $i$ .

Tap for more steps...

Step 1.1

Rewrite $- 125$ as $- 1 (125)$ .

$\frac{- 30 + \sqrt{- 1 (125)}}{5}$

Step 1.2

Rewrite $\sqrt{- 1 (125)}$ as $\sqrt{- 1} \cdot \sqrt{125}$ .

$\frac{- 30 + \sqrt{- 1} \cdot \sqrt{125}}{5}$

Step 1.3

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

$\frac{- 30 + i \cdot \sqrt{125}}{5}$

$\frac{- 30 + i \cdot \sqrt{125}}{5}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $125$ as $5^{2} \cdot 5$ .

Tap for more steps...

Step 2.1.1

Factor $25$ out of $125$ .

$\frac{- 30 + i \cdot \sqrt{25 (5)}}{5}$

Step 2.1.2

Rewrite $25$ as $5^{2}$ .

$\frac{- 30 + i \cdot \sqrt{5^{2} \cdot 5}}{5}$

$\frac{- 30 + i \cdot \sqrt{5^{2} \cdot 5}}{5}$

Step 2.2

Pull terms out from under the radical.

$\frac{- 30 + i \cdot (5 \sqrt{5})}{5}$

Step 2.3

Move $5$ to the left of $i$ .

$\frac{- 30 + 5 i \sqrt{5}}{5}$

$\frac{- 30 + 5 i \sqrt{5}}{5}$

Step 3

Cancel the common factor of $- 30 + 5 i \sqrt{5}$ and $5$ .

Tap for more steps...

Step 3.1

Factor $5$ out of $- 30$ .

$\frac{5 \cdot - 6 + 5 i \sqrt{5}}{5}$

Step 3.2

Factor $5$ out of $5 i \sqrt{5}$ .

$\frac{5 \cdot - 6 + 5 (i \sqrt{5})}{5}$

Step 3.3

Factor $5$ out of $5 (- 6) + 5 (i \sqrt{5})$ .

$\frac{5 (- 6 + i \sqrt{5})}{5}$

Step 3.4

Cancel the common factors.

Tap for more steps...

Step 3.4.1

Factor $5$ out of $5$ .

$\frac{5 (- 6 + i \sqrt{5})}{5 (1)}$

Step 3.4.2

Cancel the common factor.

$\frac{5 (- 6 + i \sqrt{5})}{5 \cdot 1}$

Step 3.4.3

Rewrite the expression.

$\frac{- 6 + i \sqrt{5}}{1}$

Step 3.4.4

Divide $- 6 + i \sqrt{5}$ by $1$ .

$- 6 + i \sqrt{5}$

$- 6 + i \sqrt{5}$

$- 6 + i \sqrt{5}$

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