Basic Math Examples

$\frac{8}{5 + \sqrt{7}}$

Step 1

Multiply $\frac{8}{5 + \sqrt{7}}$ by $\frac{5 - \sqrt{7}}{5 - \sqrt{7}}$ .

$\frac{8}{5 + \sqrt{7}} \cdot \frac{5 - \sqrt{7}}{5 - \sqrt{7}}$

Step 2

Multiply $\frac{8}{5 + \sqrt{7}}$ by $\frac{5 - \sqrt{7}}{5 - \sqrt{7}}$ .

$\frac{8 (5 - \sqrt{7})}{(5 + \sqrt{7}) (5 - \sqrt{7})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{8 (5 - \sqrt{7})}{25 - 5 \sqrt{7} + \sqrt{7} \cdot 5 - {\sqrt{7}}^{2}}$

Step 4

Simplify.

$\frac{8 (5 - \sqrt{7})}{18}$

Step 5

Cancel the common factor of $8$ and $18$ .

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Step 5.1

Factor $2$ out of $8 (5 - \sqrt{7})$ .

$\frac{2 (4 (5 - \sqrt{7}))}{18}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $18$ .

$\frac{2 (4 (5 - \sqrt{7}))}{2 (9)}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (4 (5 - \sqrt{7}))}{2 \cdot 9}$

Step 5.2.3

Rewrite the expression.

$\frac{4 (5 - \sqrt{7})}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{4 (5 - \sqrt{7})}{9}$

Decimal Form:

$1.04633275 \dots$