Trigonometry Examples

$\sqrt{1 - \frac{\frac{\sqrt{15}}{8}}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{1 - (\frac{\sqrt{15}}{8} \cdot \frac{1}{2})}$

Step 2

Multiply $\frac{\sqrt{15}}{8} \cdot \frac{1}{2}$ .

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Step 2.1

Multiply $\frac{\sqrt{15}}{8}$ by $\frac{1}{2}$ .

$\sqrt{1 - \frac{\sqrt{15}}{8 \cdot 2}}$

Step 2.2

Multiply $8$ by $2$ .

$\sqrt{1 - \frac{\sqrt{15}}{16}}$

Step 3

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

$\sqrt{\frac{16}{16} - \frac{\sqrt{15}}{16}}$

Step 4

Combine the numerators over the common denominator.

$\sqrt{\frac{16 - \sqrt{15}}{16}}$

Step 5

Rewrite $\sqrt{\frac{16 - \sqrt{15}}{16}}$ as $\frac{\sqrt{16 - \sqrt{15}}}{\sqrt{16}}$ .

$\frac{\sqrt{16 - \sqrt{15}}}{\sqrt{16}}$

Step 6

Simplify the denominator.

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Step 6.1

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

$\frac{\sqrt{16 - \sqrt{15}}}{\sqrt{4^{2}}}$

Step 6.2

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

$\frac{\sqrt{16 - \sqrt{15}}}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{16 - \sqrt{15}}}{4}$

Decimal Form:

$0.87059665 \dots$