Simplify 2\(\sqrt{3}\) - \(\frac{6}{\sqrt{3}} + \frac{3}{\sqrt{27}}\)
MATHEMATICS
WAEC 2010
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. \(\frac{1}{3}\sqrt{3}\)
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\(\sqrt{3} - 2\sqrt{3} + \frac{\sqrt{3}}{3}\)
= \(\frac{\sqrt{3}}{3} = \frac{1}{3} \sqrt{3}\)
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