Finite Math Examples

$- \frac{1}{2} + \frac{1}{10} \cdot \sqrt{165}$

Step 1

Combine $\frac{1}{10}$ and $\sqrt{165}$ .

$- \frac{1}{2} + \frac{\sqrt{165}}{10}$

Step 2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{1}{2} \cdot \frac{5}{5} + \frac{\sqrt{165}}{10}$

Step 3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$- \frac{5}{2 \cdot 5} + \frac{\sqrt{165}}{10}$

Step 3.2

Multiply $2$ by $5$ .

$- \frac{5}{10} + \frac{\sqrt{165}}{10}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 5 + \sqrt{165}}{10}$

Step 5

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- 1 (5) + \sqrt{165}}{10}$

Step 6

Factor $- 1$ out of $\sqrt{165}$ .

$\frac{- 1 (5) - 1 (- \sqrt{165})}{10}$

Step 7

Factor $- 1$ out of $- 1 (5) - 1 (- \sqrt{165})$ .

$\frac{- 1 (5 - \sqrt{165})}{10}$

Step 8

Move the negative in front of the fraction.

$- \frac{5 - \sqrt{165}}{10}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{5 - \sqrt{165}}{10}$

Decimal Form:

$0.78452325 \dots$