Trigonometry Examples

$\sqrt{- \frac{27}{4}}$

Step 1

Rewrite $- \frac{27}{4}$ as ${(\frac{3 i}{2})}^{2} \cdot 3$ .

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Step 1.1

Rewrite $- 1$ as $i^{2}$ .

$\sqrt{i^{2} \frac{27}{4}}$

Step 1.2

Factor the perfect power $3^{2}$ out of $27$ .

$\sqrt{i^{2} \frac{3^{2} \cdot 3}{4}}$

Step 1.3

Factor the perfect power $2^{2}$ out of $4$ .

$\sqrt{i^{2} \frac{3^{2} \cdot 3}{2^{2} \cdot 1}}$

Step 1.4

Rearrange the fraction $\frac{3^{2} \cdot 3}{2^{2} \cdot 1}$ .

$\sqrt{i^{2} ({(\frac{3}{2})}^{2} \cdot 3)}$

Step 1.5

Rewrite $i^{2} {(\frac{3}{2})}^{2}$ as ${(\frac{3 i}{2})}^{2}$ .

$\sqrt{{(\frac{3 i}{2})}^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

$\frac{3 i}{2} \sqrt{3}$

Step 3

Combine $\frac{3 i}{2}$ and $\sqrt{3}$ .

$\frac{3 i \sqrt{3}}{2}$