Trigonometry Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Rewrite $\sqrt{\frac{1 + \sqrt{3}}{4}}$ as $\frac{\sqrt{1 + \sqrt{3}}}{\sqrt{4}}$ .

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.82644582 \dots$