Trigonometry Examples

$\sqrt{\frac{7}{16} + 1}$

Step 1

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

$\sqrt{\frac{7}{16} + \frac{16}{16}}$

Step 2

Combine the numerators over the common denominator.

$\sqrt{\frac{7 + 16}{16}}$

Step 3

Add $7$ and $16$ .

$\sqrt{\frac{23}{16}}$

Step 4

Rewrite $\sqrt{\frac{23}{16}}$ as $\frac{\sqrt{23}}{\sqrt{16}}$ .

$\frac{\sqrt{23}}{\sqrt{16}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{23}}{\sqrt{4^{2}}}$

Step 5.2

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

$\frac{\sqrt{23}}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{23}}{4}$

Decimal Form:

$1.19895788 \dots$