Simplify 2$\sqrt{3}$ - $\frac{6}{\sqrt{3}} + \frac{3}{\sqrt{27}}$

Step 1: Analyze the question We need to simplify each term so they all share the same surd, √3.

Step 2: Simplify each term

• First term: 2√3 (already simple)
• Second term: 6/√3. Rationalize by multiplying top and bottom by √3: (6√3)/3 = 2√3
• Third term: 3/√27. Since √27 = √(9×3) = 3√3, this becomes 3/(3√3) = 1/√3 = √3/3

Step 3: Combine

2√3 − 2√3 + √3/3 = √3/3

This is (1/3)√3.

Step 4: Match the option

Check: √3 ≈ 1.732, so 2√3 ≈ 3.464, 6/√3 ≈ 3.464, and 3/√27 ≈ 3/5.196 ≈ 0.577. Then 3.464 − 3.464 + 0.577 = 0.577, and (1/3)(1.732) ≈ 0.577. ✓

Tip: In surd questions, always rationalize denominators and reduce roots like √27 to 3√3 first. Terms often cancel neatly, as the 2√3 terms did here.