Trigonometry Examples

$\sqrt{81 - \frac{47}{81}}$

Step 1

To write $81$ as a fraction with a common denominator, multiply by $\frac{81}{81}$ .

$\sqrt{81 \cdot \frac{81}{81} - \frac{47}{81}}$

Step 2

Combine $81$ and $\frac{81}{81}$ .

$\sqrt{\frac{81 \cdot 81}{81} - \frac{47}{81}}$

Step 3

Combine the numerators over the common denominator.

$\sqrt{\frac{81 \cdot 81 - 47}{81}}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $81$ by $81$ .

$\sqrt{\frac{6561 - 47}{81}}$

Step 4.2

Subtract $47$ from $6561$ .

$\sqrt{\frac{6514}{81}}$

Step 5

Rewrite $\sqrt{\frac{6514}{81}}$ as $\frac{\sqrt{6514}}{\sqrt{81}}$ .

$\frac{\sqrt{6514}}{\sqrt{81}}$

Step 6

Simplify the denominator.

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Step 6.1

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

$\frac{\sqrt{6514}}{\sqrt{9^{2}}}$

Step 6.2

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

$\frac{\sqrt{6514}}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{6514}}{9}$

Decimal Form:

$8.96770612 \dots$