Basic Math Examples

$\frac{3}{10^{2}} + \frac{2}{5^{2}} = c^{2}$

Step 1

Rewrite the equation as $c^{2} = \frac{3}{10^{2}} + \frac{2}{5^{2}}$ .

$c^{2} = \frac{3}{10^{2}} + \frac{2}{5^{2}}$

Step 2

Raise $10$ to the power of $2$ .

$c^{2} = \frac{3}{100} + \frac{2}{5^{2}}$

Step 3

Raise $5$ to the power of $2$ .

$c^{2} = \frac{3}{100} + \frac{2}{25}$

Step 4

To write $\frac{2}{25}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$c^{2} = \frac{3}{100} + \frac{2}{25} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of $100$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{2}{25}$ by $\frac{4}{4}$ .

$c^{2} = \frac{3}{100} + \frac{2 \cdot 4}{25 \cdot 4}$

Step 5.2

Multiply $25$ by $4$ .

$c^{2} = \frac{3}{100} + \frac{2 \cdot 4}{100}$

Step 6

Combine the numerators over the common denominator.

$c^{2} = \frac{3 + 2 \cdot 4}{100}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $2$ by $4$ .

$c^{2} = \frac{3 + 8}{100}$

Step 7.2

Add $3$ and $8$ .

$c^{2} = \frac{11}{100}$

Step 8

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$c = \pm \sqrt{\frac{11}{100}}$

Step 9

Simplify $\pm \sqrt{\frac{11}{100}}$ .

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Step 9.1

Rewrite $\sqrt{\frac{11}{100}}$ as $\frac{\sqrt{11}}{\sqrt{100}}$ .

$c = \pm \frac{\sqrt{11}}{\sqrt{100}}$

Step 9.2

Simplify the denominator.

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Step 9.2.1

Rewrite $100$ as $10^{2}$ .

$c = \pm \frac{\sqrt{11}}{\sqrt{10^{2}}}$

Step 9.2.2

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

$c = \pm \frac{\sqrt{11}}{10}$

Step 10

The complete solution is the result of both the positive and negative portions of the solution.

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Step 10.1

First, use the positive value of the $\pm$ to find the first solution.

$c = \frac{\sqrt{11}}{10}$

Step 10.2

Next, use the negative value of the $\pm$ to find the second solution.

$c = - \frac{\sqrt{11}}{10}$

Step 10.3

The complete solution is the result of both the positive and negative portions of the solution.

$c = \frac{\sqrt{11}}{10}, - \frac{\sqrt{11}}{10}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$c = \frac{\sqrt{11}}{10}, - \frac{\sqrt{11}}{10}$

Decimal Form:

$c = 0.33166247 \dots, - 0.33166247 \dots$