Pre-Algebra Examples

$\frac{8}{\sqrt{14} + \sqrt{6}}$

Step 1

Multiply $\frac{8}{\sqrt{14} + \sqrt{6}}$ by $\frac{\sqrt{14} - \sqrt{6}}{\sqrt{14} - \sqrt{6}}$ .

$\frac{8}{\sqrt{14} + \sqrt{6}} \cdot \frac{\sqrt{14} - \sqrt{6}}{\sqrt{14} - \sqrt{6}}$

Step 2

Multiply $\frac{8}{\sqrt{14} + \sqrt{6}}$ by $\frac{\sqrt{14} - \sqrt{6}}{\sqrt{14} - \sqrt{6}}$ .

$\frac{8 (\sqrt{14} - \sqrt{6})}{(\sqrt{14} + \sqrt{6}) (\sqrt{14} - \sqrt{6})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{8 (\sqrt{14} - \sqrt{6})}{{\sqrt{14}}^{2} - \sqrt{84} + \sqrt{84} - {\sqrt{6}}^{2}}$

Step 4

Simplify.

$\frac{8 (\sqrt{14} - \sqrt{6})}{8}$

Step 5

Cancel the common factor of $8$ .

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Step 5.1

Cancel the common factor.

$\frac{8 (\sqrt{14} - \sqrt{6})}{8}$

Step 5.2

Divide $\sqrt{14} - \sqrt{6}$ by $1$ .

$\sqrt{14} - \sqrt{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt{14} - \sqrt{6}$

Decimal Form:

$1.29216764 \dots$