Pre-Algebra Examples

$\frac{3}{7 + \sqrt{3}}$

Step 1

Multiply $\frac{3}{7 + \sqrt{3}}$ by $\frac{7 - \sqrt{3}}{7 - \sqrt{3}}$ .

$\frac{3}{7 + \sqrt{3}} \cdot \frac{7 - \sqrt{3}}{7 - \sqrt{3}}$

Step 2

Multiply $\frac{3}{7 + \sqrt{3}}$ by $\frac{7 - \sqrt{3}}{7 - \sqrt{3}}$ .

$\frac{3 (7 - \sqrt{3})}{(7 + \sqrt{3}) (7 - \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{3 (7 - \sqrt{3})}{49 - 7 \sqrt{3} + \sqrt{3} \cdot 7 - {\sqrt{3}}^{2}}$

Step 4

Simplify.

$\frac{3 (7 - \sqrt{3})}{46}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (7 - \sqrt{3})}{46}$

Decimal Form:

$0.34356190 \dots$