Trigonometry Examples

$\sqrt{1 - \frac{- \sqrt{7}}{\frac{9}{2}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{1 - (- \sqrt{7} \frac{2}{9})}$

Step 2

Combine $\frac{2}{9}$ and $\sqrt{7}$ .

$\sqrt{1 - - \frac{2 \sqrt{7}}{9}}$

Step 3

Multiply $- - \frac{2 \sqrt{7}}{9}$ .

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Step 3.1

Multiply $- 1$ by $- 1$ .

$\sqrt{1 + 1 \frac{2 \sqrt{7}}{9}}$

Step 3.2

Multiply $\frac{2 \sqrt{7}}{9}$ by $1$ .

$\sqrt{1 + \frac{2 \sqrt{7}}{9}}$

Step 4

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

$\sqrt{\frac{9}{9} + \frac{2 \sqrt{7}}{9}}$

Step 5

Combine the numerators over the common denominator.

$\sqrt{\frac{9 + 2 \sqrt{7}}{9}}$

Step 6

Rewrite $\sqrt{\frac{9 + 2 \sqrt{7}}{9}}$ as $\frac{\sqrt{9 + 2 \sqrt{7}}}{\sqrt{9}}$ .

$\frac{\sqrt{9 + 2 \sqrt{7}}}{\sqrt{9}}$

Step 7

Simplify the denominator.

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Step 7.1

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{9 + 2 \sqrt{7}}}{\sqrt{3^{2}}}$

Step 7.2

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

$\frac{\sqrt{9 + 2 \sqrt{7}}}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{9 + 2 \sqrt{7}}}{3}$

Decimal Form:

$1.26013679 \dots$