Trigonometry Examples

$\sqrt{\frac{1}{9}} + \frac{1}{4}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\sqrt{\frac{1}{9}}$ as $\frac{\sqrt{1}}{\sqrt{9}}$ .

$\frac{\sqrt{1}}{\sqrt{9}} + \frac{1}{4}$

Step 1.2

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{9}} + \frac{1}{4}$

Step 1.3

Simplify the denominator.

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Step 1.3.1

Rewrite $9$ as $3^{2}$ .

$\frac{1}{\sqrt{3^{2}}} + \frac{1}{4}$

Step 1.3.2

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

$\frac{1}{3} + \frac{1}{4}$

Step 2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{3} \cdot \frac{4}{4} + \frac{1}{4}$

Step 3

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{3} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$\frac{4}{3 \cdot 4} + \frac{1}{4} \cdot \frac{3}{3}$

Step 4.2

Multiply $3$ by $4$ .

$\frac{4}{12} + \frac{1}{4} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{4}{12} + \frac{3}{4 \cdot 3}$

Step 4.4

Multiply $4$ by $3$ .

$\frac{4}{12} + \frac{3}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 + 3}{12}$

Step 6

Add $4$ and $3$ .

$\frac{7}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{12}$

Decimal Form:

$0.58\overline{3}$