Trigonometry Examples

$\sqrt{\frac{1 + \frac{1}{8}}{2}}$

Step 1

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

$\sqrt{\frac{\frac{8}{8} + \frac{1}{8}}{2}}$

Step 2

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{8 + 1}{8}}{2}}$

Step 3

Add $8$ and $1$ .

$\sqrt{\frac{\frac{9}{8}}{2}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{9}{8} \cdot \frac{1}{2}}$

Step 5

Multiply $\frac{9}{8} \cdot \frac{1}{2}$ .

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Step 5.1

Multiply $\frac{9}{8}$ by $\frac{1}{2}$ .

$\sqrt{\frac{9}{8 \cdot 2}}$

Step 5.2

Multiply $8$ by $2$ .

$\sqrt{\frac{9}{16}}$

Step 6

Rewrite $\sqrt{\frac{9}{16}}$ as $\frac{\sqrt{9}}{\sqrt{16}}$ .

$\frac{\sqrt{9}}{\sqrt{16}}$

Step 7

Simplify the numerator.

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Step 7.1

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

$\frac{\sqrt{3^{2}}}{\sqrt{16}}$

Step 7.2

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

$\frac{3}{\sqrt{16}}$

Step 8

Simplify the denominator.

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Step 8.1

Rewrite $16$ as $4^{2}$ .

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

Step 8.2

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

$\frac{3}{4}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$