Basic Math Examples

$\frac{10}{6 + \sqrt{6}}$

Step 1

Multiply $\frac{10}{6 + \sqrt{6}}$ by $\frac{6 - \sqrt{6}}{6 - \sqrt{6}}$ .

$\frac{10}{6 + \sqrt{6}} \cdot \frac{6 - \sqrt{6}}{6 - \sqrt{6}}$

Step 2

Multiply $\frac{10}{6 + \sqrt{6}}$ by $\frac{6 - \sqrt{6}}{6 - \sqrt{6}}$ .

$\frac{10 (6 - \sqrt{6})}{(6 + \sqrt{6}) (6 - \sqrt{6})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{10 (6 - \sqrt{6})}{36 - 6 \sqrt{6} + \sqrt{6} \cdot 6 - {\sqrt{6}}^{2}}$

Step 4

Simplify.

$\frac{10 (6 - \sqrt{6})}{30}$

Step 5

Cancel the common factors.

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Step 5.1

Factor $10$ out of $30$ .

$\frac{10 (6 - \sqrt{6})}{10 \cdot 3}$

Step 5.2

Cancel the common factor.

$\frac{10 (6 - \sqrt{6})}{10 \cdot 3}$

Step 5.3

Rewrite the expression.

$\frac{6 - \sqrt{6}}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{6 - \sqrt{6}}{3}$

Decimal Form:

$1.18350341 \dots$