Trigonometry Examples

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

Step 1

Simplify the expression.

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Step 1.1

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

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

Step 1.2

Combine the numerators over the common denominator.

$\sqrt{\frac{1}{2} \cdot \frac{8 - 7}{8}}$

Step 1.3

Subtract $7$ from $8$ .

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

Step 2

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

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

Step 3

Multiply $2$ by $8$ .

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

Step 4

Rewrite $\sqrt{\frac{1}{16}}$ as $\frac{\sqrt{1}}{\sqrt{16}}$ .

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

Step 5

Any root of $1$ is $1$ .

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

Step 6

Simplify the denominator.

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Step 6.1

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

$\frac{1}{\sqrt{4^{2}}}$

Step 6.2

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

$\frac{1}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$