Evaluate 4/(3 square root of 3-2)

$\frac{4}{3 \sqrt{3} - 2}$

Step 1

Multiply $\frac{4}{3 \sqrt{3} - 2}$ by $\frac{3 \sqrt{3} + 2}{3 \sqrt{3} + 2}$ .

$\frac{4}{3 \sqrt{3} - 2} \cdot \frac{3 \sqrt{3} + 2}{3 \sqrt{3} + 2}$

Step 2

Multiply $\frac{4}{3 \sqrt{3} - 2}$ by $\frac{3 \sqrt{3} + 2}{3 \sqrt{3} + 2}$ .

$\frac{4 (3 \sqrt{3} + 2)}{(3 \sqrt{3} - 2) (3 \sqrt{3} + 2)}$

Step 3

Expand the denominator using the FOIL method.

$\frac{4 (3 \sqrt{3} + 2)}{9 {\sqrt{3}}^{2} + 6 \sqrt{3} - 6 \sqrt{3} - 4}$

Step 4

Simplify.

$\frac{4 (3 \sqrt{3} + 2)}{23}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4 (3 \sqrt{3} + 2)}{23}$

Decimal Form:

$1.25150476 \dots$