Simplify 2\(\sqrt{3}\) - \(\frac{6}{\sqrt{3}} + \frac{3}{\sqrt{27}}\)
A. 1
B. \(\frac{1}{3}\sqrt{3}\)
C. 2\(\sqrt{3} - 5\frac{2}{3}\)
D. 6\(\sqrt{3}\) - 17
Correct Answer: B
Explanation
2\(\sqrt{3}\) - \(\frac{6}{\sqrt{3}} + \frac{3}{\sqrt{27}}\)
= 2\(\sqrt{3} - \frac{6}{\sqrt{3}} + \frac{3}{\sqrt{9 \times 3}}\)
= 2\(\sqrt{3} - \frac{6}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} + \frac{3}{3\sqrt{3}}\)
= 2\(\sqrt{3} = 6 \frac{\sqrt{3}}{3} + \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\)
= 2\(\sqrt{3} - 2\sqrt{3} + \frac{\sqrt{3}}{3}\)
= \(\frac{\sqrt{3}}{3} = \frac{1}{3} \sqrt{3}\)
