Trigonometry Examples

$\sqrt{\frac{- 12}{25}}$

Step 1

Move the negative in front of the fraction.

$\sqrt{- \frac{12}{25}}$

Step 2

Rewrite $- \frac{12}{25}$ as ${(\frac{2 i}{5})}^{2} \cdot 3$ .

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Step 2.1

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

$\sqrt{i^{2} \frac{12}{25}}$

Step 2.2

Factor the perfect power $2^{2}$ out of $12$ .

$\sqrt{i^{2} \frac{2^{2} \cdot 3}{25}}$

Step 2.3

Factor the perfect power $5^{2}$ out of $25$ .

$\sqrt{i^{2} \frac{2^{2} \cdot 3}{5^{2} \cdot 1}}$

Step 2.4

Rearrange the fraction $\frac{2^{2} \cdot 3}{5^{2} \cdot 1}$ .

$\sqrt{i^{2} ({(\frac{2}{5})}^{2} \cdot 3)}$

Step 2.5

Rewrite $i^{2} {(\frac{2}{5})}^{2}$ as ${(\frac{2 i}{5})}^{2}$ .

$\sqrt{{(\frac{2 i}{5})}^{2} \cdot 3}$

Step 3

Pull terms out from under the radical.

$\frac{2 i}{5} \sqrt{3}$

Step 4

Combine $\frac{2 i}{5}$ and $\sqrt{3}$ .

$\frac{2 i \sqrt{3}}{5}$