Trigonometry Examples

$\sqrt{\frac{1 - (\frac{- 7}{25})}{2}}$

Step 1

Move the negative in front of the fraction.

$\sqrt{\frac{1 - - \frac{7}{25}}{2}}$

Step 2

Multiply $- - \frac{7}{25}$ .

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Step 2.1

Multiply $- 1$ by $- 1$ .

$\sqrt{\frac{1 + 1 (\frac{7}{25})}{2}}$

Step 2.2

Multiply $\frac{7}{25}$ by $1$ .

$\sqrt{\frac{1 + \frac{7}{25}}{2}}$

Step 3

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

$\sqrt{\frac{\frac{25}{25} + \frac{7}{25}}{2}}$

Step 4

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{25 + 7}{25}}{2}}$

Step 5

Add $25$ and $7$ .

$\sqrt{\frac{\frac{32}{25}}{2}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{32}{25} \cdot \frac{1}{2}}$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Factor $2$ out of $32$ .

$\sqrt{\frac{2 (16)}{25} \cdot \frac{1}{2}}$

Step 7.2

Cancel the common factor.

$\sqrt{\frac{2 \cdot 16}{25} \cdot \frac{1}{2}}$

Step 7.3

Rewrite the expression.

$\sqrt{\frac{16}{25}}$

Step 8

Rewrite $\sqrt{\frac{16}{25}}$ as $\frac{\sqrt{16}}{\sqrt{25}}$ .

$\frac{\sqrt{16}}{\sqrt{25}}$

Step 9

Simplify the numerator.

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Step 9.1

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

$\frac{\sqrt{4^{2}}}{\sqrt{25}}$

Step 9.2

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

$\frac{4}{\sqrt{25}}$

Step 10

Simplify the denominator.

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Step 10.1

Rewrite $25$ as $5^{2}$ .

$\frac{4}{\sqrt{5^{2}}}$

Step 10.2

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

$\frac{4}{5}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{5}$

Decimal Form:

$0.8$