Trigonometry Examples

$\sqrt{\frac{1 + \frac{11}{61}}{1 + \frac{11}{61}}}$

Step 1

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

$\sqrt{\frac{\frac{61}{61} + \frac{11}{61}}{1 + \frac{11}{61}}}$

Step 2

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{61 + 11}{61}}{1 + \frac{11}{61}}}$

Step 3

Add $61$ and $11$ .

$\sqrt{\frac{\frac{72}{61}}{1 + \frac{11}{61}}}$

Step 4

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

$\sqrt{\frac{\frac{72}{61}}{\frac{61}{61} + \frac{11}{61}}}$

Step 5

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{72}{61}}{\frac{61 + 11}{61}}}$

Step 6

Add $61$ and $11$ .

$\sqrt{\frac{\frac{72}{61}}{\frac{72}{61}}}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Reduce the expression $\frac{\frac{72}{61}}{\frac{72}{61}}$ by cancelling the common factors.

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Step 7.1.1

Cancel the common factor.

$\sqrt{\frac{\frac{72}{61}}{\frac{72}{61}}}$

Step 7.1.2

Rewrite the expression.

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

Step 7.2

Rewrite the expression.

$\sqrt{1}$

Step 8

Any root of $1$ is $1$ .

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Step 8.1

Reduce the expression $\frac{\frac{72}{61}}{\frac{72}{61}}$ by cancelling the common factors.

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Step 8.1.1

Cancel the common factor.

$\frac{\frac{72}{61}}{\frac{72}{61}}$

Step 8.1.2

Rewrite the expression.

$\frac{1}{1}$

Step 8.2

Rewrite the expression.

$1$