Trigonometry Examples

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

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

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

Step 2

Multiply

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

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

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Step 2.1

Multiply

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

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

\frac{1}{2}

$\frac{1}{2}$ .

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

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

Step 2.2

Multiply

8

$8$ by

2

$2$ .

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

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

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

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

Step 3

Rewrite

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

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

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

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

\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

$16$ as

4^{2}

$4^{2}$ .

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

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

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

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

Decimal Form:

0.50787650 \dots

$0.50787650 \dots$