Trigonometry Examples

$\sqrt{\frac{1 + \frac{1}{9}}{2}}$

Step 1

Write $1$ as a fraction with a common denominator.

$\sqrt{\frac{\frac{9}{9} + \frac{1}{9}}{2}}$

Step 2

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{9 + 1}{9}}{2}}$

Step 3

Add $9$ and $1$ .

$\sqrt{\frac{\frac{10}{9}}{2}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{10}{9} \cdot \frac{1}{2}}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $10$ .

$\sqrt{\frac{2 (5)}{9} \cdot \frac{1}{2}}$

Step 5.2

Cancel the common factor.

$\sqrt{\frac{2 \cdot 5}{9} \cdot \frac{1}{2}}$

Step 5.3

Rewrite the expression.

$\sqrt{\frac{5}{9}}$

Step 6

Rewrite $\sqrt{\frac{5}{9}}$ as $\frac{\sqrt{5}}{\sqrt{9}}$ .

$\frac{\sqrt{5}}{\sqrt{9}}$

Step 7

Simplify the denominator.

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Step 7.1

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

$\frac{\sqrt{5}}{\sqrt{3^{2}}}$

Step 7.2

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

$\frac{\sqrt{5}}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{5}}{3}$

Decimal Form:

$0.74535599 \dots$