Trigonometry Examples

$\sqrt{\frac{1 - (- \frac{7}{8})}{2}}$

Step 1

Multiply $- (- \frac{7}{8})$ .

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Step 1.1

Multiply $- 1$ by $- 1$ .

$\sqrt{\frac{1 + 1 (\frac{7}{8})}{2}}$

Step 1.2

Multiply $\frac{7}{8}$ by $1$ .

$\sqrt{\frac{1 + \frac{7}{8}}{2}}$

Step 2

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

$\sqrt{\frac{\frac{8}{8} + \frac{7}{8}}{2}}$

Step 3

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{8 + 7}{8}}{2}}$

Step 4

Add $8$ and $7$ .

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

Step 5

Multiply the numerator by the reciprocal of the denominator.

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Multiply $8$ by $2$ .

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

Step 7

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

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

Step 8

Simplify the denominator.

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Step 8.1

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

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

Step 8.2

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

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

Step 9

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.96824583 \dots$