Trigonometry Examples

$\sqrt{1 + \frac{16}{121}}$

Step 1

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

$\sqrt{\frac{121}{121} + \frac{16}{121}}$

Step 2

Combine the numerators over the common denominator.

$\sqrt{\frac{121 + 16}{121}}$

Step 3

Add $121$ and $16$ .

$\sqrt{\frac{137}{121}}$

Step 4

Rewrite $\sqrt{\frac{137}{121}}$ as $\frac{\sqrt{137}}{\sqrt{121}}$ .

$\frac{\sqrt{137}}{\sqrt{121}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $121$ as $11^{2}$ .

$\frac{\sqrt{137}}{\sqrt{11^{2}}}$

Step 5.2

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

$\frac{\sqrt{137}}{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{137}}{11}$

Decimal Form:

$1.06406362 \dots$