Pre-Algebra Examples

$\frac{- 35 - \sqrt{- 75}}{5}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 75$ as $- 1 (75)$ .

$\frac{- 35 - \sqrt{- 1 (75)}}{5}$

Step 1.2

Rewrite $\sqrt{- 1 (75)}$ as $\sqrt{- 1} \cdot \sqrt{75}$ .

$\frac{- 35 - (\sqrt{- 1} \cdot \sqrt{75})}{5}$

Step 1.3

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

$\frac{- 35 - (i \cdot \sqrt{75})}{5}$

$\frac{- 35 - (i \cdot \sqrt{75})}{5}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 2.1.1

Factor $25$ out of $75$ .

$\frac{- 35 - i \cdot \sqrt{25 (3)}}{5}$

Step 2.1.2

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

$\frac{- 35 - i \cdot \sqrt{5^{2} \cdot 3}}{5}$

$\frac{- 35 - i \cdot \sqrt{5^{2} \cdot 3}}{5}$

Step 2.2

Pull terms out from under the radical.

$\frac{- 35 - i \cdot (5 \sqrt{3})}{5}$

Step 2.3

Multiply $5$ by $- 1$ .

$\frac{- 35 - 5 i \sqrt{3}}{5}$

$\frac{- 35 - 5 i \sqrt{3}}{5}$

Step 3

Cancel the common factor of $- 35 - 5 i \sqrt{3}$ and $5$ .

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Step 3.1

Factor $5$ out of $- 35$ .

$\frac{5 \cdot - 7 - 5 i \sqrt{3}}{5}$

Step 3.2

Factor $5$ out of $- 5 i \sqrt{3}$ .

$\frac{5 \cdot - 7 + 5 (- i \sqrt{3})}{5}$

Step 3.3

Factor $5$ out of $5 (- 7) + 5 (- i \sqrt{3})$ .

$\frac{5 (- 7 - i \sqrt{3})}{5}$

Step 3.4

Cancel the common factors.

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Step 3.4.1

Factor $5$ out of $5$ .

$\frac{5 (- 7 - i \sqrt{3})}{5 (1)}$

Step 3.4.2

Cancel the common factor.

$\frac{5 (- 7 - i \sqrt{3})}{5 \cdot 1}$

Step 3.4.3

Rewrite the expression.

$\frac{- 7 - i \sqrt{3}}{1}$

Step 3.4.4

Divide $- 7 - i \sqrt{3}$ by $1$ .

$- 7 - i \sqrt{3}$

$- 7 - i \sqrt{3}$

$- 7 - i \sqrt{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$