Trigonometry Examples

$\frac{8 + \sqrt{- 27}}{6}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 27$ as $- 1 (27)$ .

$\frac{8 + \sqrt{- 1 (27)}}{6}$

Step 1.2

Rewrite $\sqrt{- 1 (27)}$ as $\sqrt{- 1} \cdot \sqrt{27}$ .

$\frac{8 + \sqrt{- 1} \cdot \sqrt{27}}{6}$

Step 1.3

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

$\frac{8 + i \cdot \sqrt{27}}{6}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 2.1.1

Factor $9$ out of $27$ .

$\frac{8 + i \cdot \sqrt{9 (3)}}{6}$

Step 2.1.2

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

$\frac{8 + i \cdot \sqrt{3^{2} \cdot 3}}{6}$

Step 2.2

Pull terms out from under the radical.

$\frac{8 + i \cdot (3 \sqrt{3})}{6}$

Step 2.3

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

$\frac{8 + 3 i \sqrt{3}}{6}$