Trigonometry Examples

$\frac{\sqrt{- 175}}{\sqrt{7}}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 175$ as $- 1 (175)$ .

$\frac{\sqrt{- 1 (175)}}{\sqrt{7}}$

Step 1.2

Rewrite $\sqrt{- 1 (175)}$ as $\sqrt{- 1} \cdot \sqrt{175}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{175}}{\sqrt{7}}$

Step 1.3

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

$\frac{i \cdot \sqrt{175}}{\sqrt{7}}$

Step 2

Combine $\sqrt{175}$ and $\sqrt{7}$ into a single radical.

$i \cdot \sqrt{\frac{175}{7}}$

Step 3

Simplify the expression.

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Step 3.1

Divide $175$ by $7$ .

$i \cdot \sqrt{25}$

Step 3.2

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

$i \cdot \sqrt{5^{2}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$i \cdot 5$

Step 5

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

$5 i$