Trigonometry Examples

$\sqrt{1 - \frac{81}{1681}}$

Step 1

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

$\sqrt{\frac{1681}{1681} - \frac{81}{1681}}$

Step 2

Combine the numerators over the common denominator.

$\sqrt{\frac{1681 - 81}{1681}}$

Step 3

Subtract $81$ from $1681$ .

$\sqrt{\frac{1600}{1681}}$

Step 4

Rewrite $\sqrt{\frac{1600}{1681}}$ as $\frac{\sqrt{1600}}{\sqrt{1681}}$ .

$\frac{\sqrt{1600}}{\sqrt{1681}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $1600$ as $40^{2}$ .

$\frac{\sqrt{40^{2}}}{\sqrt{1681}}$

Step 5.2

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

$\frac{40}{\sqrt{1681}}$

Step 6

Simplify the denominator.

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Step 6.1

Rewrite $1681$ as $41^{2}$ .

$\frac{40}{\sqrt{41^{2}}}$

Step 6.2

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

$\frac{40}{41}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{40}{41}$

Decimal Form:

$0.\overline{97560}$