Trigonometry Examples

$\frac{8}{\sqrt{3} - \sqrt{11}}$

Step 1

Multiply $\frac{8}{\sqrt{3} - \sqrt{11}}$ by $\frac{\sqrt{3} + \sqrt{11}}{\sqrt{3} + \sqrt{11}}$ .

$\frac{8}{\sqrt{3} - \sqrt{11}} \cdot \frac{\sqrt{3} + \sqrt{11}}{\sqrt{3} + \sqrt{11}}$

Step 2

Multiply $\frac{8}{\sqrt{3} - \sqrt{11}}$ by $\frac{\sqrt{3} + \sqrt{11}}{\sqrt{3} + \sqrt{11}}$ .

$\frac{8 (\sqrt{3} + \sqrt{11})}{(\sqrt{3} - \sqrt{11}) (\sqrt{3} + \sqrt{11})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{8 (\sqrt{3} + \sqrt{11})}{{\sqrt{3}}^{2} + \sqrt{33} - \sqrt{33} - {\sqrt{11}}^{2}}$

Step 4

Simplify.

$\frac{8 (\sqrt{3} + \sqrt{11})}{- 8}$

Step 5

Simplify the expression.

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Step 5.1

Move the negative one from the denominator of $\frac{\sqrt{3} + \sqrt{11}}{- 1}$ .

$- 1 \cdot (\sqrt{3} + \sqrt{11})$

Step 5.2

Rewrite $- 1 \cdot (\sqrt{3} + \sqrt{11})$ as $- (\sqrt{3} + \sqrt{11})$ .

$- (\sqrt{3} + \sqrt{11})$

Step 6

Apply the distributive property.

$- \sqrt{3} - \sqrt{11}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{3} - \sqrt{11}$

Decimal Form:

$- 5.04867559 \dots$