Algebra Examples

$\frac{- 6 + \sqrt{- 54}}{3}$

Step 1

Pull out imaginary unit $i$ .

Tap for more steps...

Step 1.1

Rewrite $- 54$ as $- 1 (54)$ .

$\frac{- 6 + \sqrt{- 1 (54)}}{3}$

Step 1.2

Rewrite $\sqrt{- 1 (54)}$ as $\sqrt{- 1} \cdot \sqrt{54}$ .

$\frac{- 6 + \sqrt{- 1} \cdot \sqrt{54}}{3}$

Step 1.3

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

$\frac{- 6 + i \cdot \sqrt{54}}{3}$

$\frac{- 6 + i \cdot \sqrt{54}}{3}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $54$ as $3^{2} \cdot 6$ .

Tap for more steps...

Step 2.1.1

Factor $9$ out of $54$ .

$\frac{- 6 + i \cdot \sqrt{9 (6)}}{3}$

Step 2.1.2

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

$\frac{- 6 + i \cdot \sqrt{3^{2} \cdot 6}}{3}$

$\frac{- 6 + i \cdot \sqrt{3^{2} \cdot 6}}{3}$

Step 2.2

Pull terms out from under the radical.

$\frac{- 6 + i \cdot (3 \sqrt{6})}{3}$

Step 2.3

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

$\frac{- 6 + 3 i \sqrt{6}}{3}$

$\frac{- 6 + 3 i \sqrt{6}}{3}$

Step 3

Cancel the common factor of $- 6 + 3 i \sqrt{6}$ and $3$ .

Tap for more steps...

Step 3.1

Factor $3$ out of $- 6$ .

$\frac{3 \cdot - 2 + 3 i \sqrt{6}}{3}$

Step 3.2

Factor $3$ out of $3 i \sqrt{6}$ .

$\frac{3 \cdot - 2 + 3 (i \sqrt{6})}{3}$

Step 3.3

Factor $3$ out of $3 (- 2) + 3 (i \sqrt{6})$ .

$\frac{3 (- 2 + i \sqrt{6})}{3}$

Step 3.4

Cancel the common factors.

Tap for more steps...

Step 3.4.1

Factor $3$ out of $3$ .

$\frac{3 (- 2 + i \sqrt{6})}{3 (1)}$

Step 3.4.2

Cancel the common factor.

$\frac{3 (- 2 + i \sqrt{6})}{3 \cdot 1}$

Step 3.4.3

Rewrite the expression.

$\frac{- 2 + i \sqrt{6}}{1}$

Step 3.4.4

Divide $- 2 + i \sqrt{6}$ by $1$ .

$- 2 + i \sqrt{6}$

$- 2 + i \sqrt{6}$

$- 2 + i \sqrt{6}$

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