#### Answer

$\frac{\sqrt{3}}{18}$

#### Work Step by Step

Step 1: $\frac{\sqrt{75}}{9} - \frac{\sqrt{3}}{2}$
Step 2: $\frac{2 \times \sqrt{75}}{18} - \frac{9 \times \sqrt{3}}{18}$
Step 3: $\frac{2\times \sqrt{25}\times\sqrt{3}}{18} - \frac{9\sqrt{3}}{18}$
Step 4: $\frac{2\times 5\times\sqrt{3}}{18} - \frac{9\sqrt{3}}{18}$
Step 5: $\frac{10\sqrt{3}}{18} - \frac{9\sqrt{3}}{18}$
Answer: $\frac{\sqrt{3}}{18}$