Trigonometry Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Multiply $8$ by $2$ .

$\sqrt{\frac{8 - \sqrt{15}}{16}}$

Step 3

Rewrite $\sqrt{\frac{8 - \sqrt{15}}{16}}$ as $\frac{\sqrt{8 - \sqrt{15}}}{\sqrt{16}}$ .

$\frac{\sqrt{8 - \sqrt{15}}}{\sqrt{16}}$

Step 4

Simplify the denominator.

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Step 4.1

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

$\frac{\sqrt{8 - \sqrt{15}}}{\sqrt{4^{2}}}$

Step 4.2

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

$\frac{\sqrt{8 - \sqrt{15}}}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{8 - \sqrt{15}}}{4}$

Decimal Form:

$0.50787650 \dots$