Basic Math Examples

$\frac{13}{5 + 2 \sqrt{3}}$

Step 1

Multiply $\frac{13}{5 + 2 \sqrt{3}}$ by $\frac{5 - 2 \sqrt{3}}{5 - 2 \sqrt{3}}$ .

$\frac{13}{5 + 2 \sqrt{3}} \cdot \frac{5 - 2 \sqrt{3}}{5 - 2 \sqrt{3}}$

Step 2

Multiply $\frac{13}{5 + 2 \sqrt{3}}$ by $\frac{5 - 2 \sqrt{3}}{5 - 2 \sqrt{3}}$ .

$\frac{13 (5 - 2 \sqrt{3})}{(5 + 2 \sqrt{3}) (5 - 2 \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{13 (5 - 2 \sqrt{3})}{25 - 10 \sqrt{3} + 10 \sqrt{3} - 4 {\sqrt{3}}^{2}}$

Step 4

Simplify.

$\frac{13 (5 - 2 \sqrt{3})}{13}$

Step 5

Cancel the common factor of $13$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

$\frac{13 (5 - 2 \sqrt{3})}{13}$

Step 5.2

Divide $5 - 2 \sqrt{3}$ by $1$ .

$5 - 2 \sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$5 - 2 \sqrt{3}$

Decimal Form:

$1.53589838 \dots$