Basic Math Examples

\frac{9}{5 + \sqrt{3}}

$\frac{9}{5 + \sqrt{3}}$

Step 1

Multiply

\frac{9}{5 + \sqrt{3}}

$\frac{9}{5 + \sqrt{3}}$ by

\frac{5 - \sqrt{3}}{5 - \sqrt{3}}

$\frac{5 - \sqrt{3}}{5 - \sqrt{3}}$ .

\frac{9}{5 + \sqrt{3}} \cdot \frac{5 - \sqrt{3}}{5 - \sqrt{3}}

$\frac{9}{5 + \sqrt{3}} \cdot \frac{5 - \sqrt{3}}{5 - \sqrt{3}}$

Step 2

Multiply

\frac{9}{5 + \sqrt{3}}

$\frac{9}{5 + \sqrt{3}}$ by

\frac{5 - \sqrt{3}}{5 - \sqrt{3}}

$\frac{5 - \sqrt{3}}{5 - \sqrt{3}}$ .

\frac{9 (5 - \sqrt{3})}{(5 + \sqrt{3}) (5 - \sqrt{3})}

$\frac{9 (5 - \sqrt{3})}{(5 + \sqrt{3}) (5 - \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

\frac{9 (5 - \sqrt{3})}{25 - 5 \sqrt{3} + \sqrt{3} \cdot 5 - {\sqrt{3}}^{2}}

$\frac{9 (5 - \sqrt{3})}{25 - 5 \sqrt{3} + \sqrt{3} \cdot 5 - {\sqrt{3}}^{2}}$

Step 4

Simplify.

\frac{9 (5 - \sqrt{3})}{22}

$\frac{9 (5 - \sqrt{3})}{22}$

Step 5

The result can be shown in multiple forms.

Exact Form:

\frac{9 (5 - \sqrt{3})}{22}

$\frac{9 (5 - \sqrt{3})}{22}$

Decimal Form:

1.33688830 \dots

$1.33688830 \dots$