Trigonometry Examples

$\sqrt{1 - \frac{25}{81}}$

Step 1

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

$\sqrt{\frac{81}{81} - \frac{25}{81}}$

Step 2

Combine the numerators over the common denominator.

$\sqrt{\frac{81 - 25}{81}}$

Step 3

Subtract $25$ from $81$ .

$\sqrt{\frac{56}{81}}$

Step 4

Rewrite $\sqrt{\frac{56}{81}}$ as $\frac{\sqrt{56}}{\sqrt{81}}$ .

$\frac{\sqrt{56}}{\sqrt{81}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $56$ as $2^{2} \cdot 14$ .

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Step 5.1.1

Factor $4$ out of $56$ .

$\frac{\sqrt{4 (14)}}{\sqrt{81}}$

Step 5.1.2

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

$\frac{\sqrt{2^{2} \cdot 14}}{\sqrt{81}}$

Step 5.2

Pull terms out from under the radical.

$\frac{2 \sqrt{14}}{\sqrt{81}}$

Step 6

Simplify the denominator.

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Step 6.1

Rewrite $81$ as $9^{2}$ .

$\frac{2 \sqrt{14}}{\sqrt{9^{2}}}$

Step 6.2

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

$\frac{2 \sqrt{14}}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{14}}{9}$

Decimal Form:

$0.83147941 \dots$