Algebra Examples

$\frac{- 20 + \sqrt{- 50}}{60}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 50$ as $- 1 (50)$ .

$\frac{- 20 + \sqrt{- 1 (50)}}{60}$

Step 1.2

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$\frac{- 20 + \sqrt{- 1} \cdot \sqrt{50}}{60}$

Step 1.3

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

$\frac{- 20 + i \cdot \sqrt{50}}{60}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 2.1.1

Factor $25$ out of $50$ .

$\frac{- 20 + i \cdot \sqrt{25 (2)}}{60}$

Step 2.1.2

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

$\frac{- 20 + i \cdot \sqrt{5^{2} \cdot 2}}{60}$

Step 2.2

Pull terms out from under the radical.

$\frac{- 20 + i \cdot (5 \sqrt{2})}{60}$

Step 2.3

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

$\frac{- 20 + 5 i \sqrt{2}}{60}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $- 20 + 5 i \sqrt{2}$ and $60$ .

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Step 3.1.1

Factor $5$ out of $- 20$ .

$\frac{5 \cdot - 4 + 5 i \sqrt{2}}{60}$

Step 3.1.2

Factor $5$ out of $5 i \sqrt{2}$ .

$\frac{5 \cdot - 4 + 5 (i \sqrt{2})}{60}$

Step 3.1.3

Factor $5$ out of $5 \cdot - 4 + 5 (i \sqrt{2})$ .

$\frac{5 \cdot (- 4 + i \sqrt{2})}{60}$

Step 3.1.4

Cancel the common factors.

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Step 3.1.4.1

Factor $5$ out of $60$ .

$\frac{5 \cdot (- 4 + i \sqrt{2})}{5 (12)}$

Step 3.1.4.2

Cancel the common factor.

$\frac{5 \cdot (- 4 + i \sqrt{2})}{5 \cdot 12}$

Step 3.1.4.3

Rewrite the expression.

$\frac{- 4 + i \sqrt{2}}{12}$

Step 3.2

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- 1 (4) + i \sqrt{2}}{12}$

Step 3.3

Factor $- 1$ out of $i \sqrt{2}$ .

$\frac{- 1 (4) - (- i \sqrt{2})}{12}$

Step 3.4

Factor $- 1$ out of $- 1 (4) - (- i \sqrt{2})$ .

$\frac{- 1 (4 - i \sqrt{2})}{12}$

Step 3.5

Move the negative in front of the fraction.

$- \frac{4 - i \sqrt{2}}{12}$