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Simplify \(\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}}\)

Further Mathematics
WAEC 2008

Simplify \(\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}}\)

  • A. \(3\sqrt{2}\)
  • B. \(5\sqrt{2}\)
  • C. \(\frac{5\sqrt{2}}{2}\)
  • D. \(\frac{3\sqrt{2}}{2}\)
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Correct Answer: Option C
Explanation

\(\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}} = \frac{\sqrt{3} + 4\sqrt{3}}{\sqrt{6}}\)

\(\frac{5\sqrt{3}}{\sqrt{6} = \frac{5\sqrt{3} \times \sqrt{6}}{\sqrt{6} \times \sqrt{6}}\)

\(\frac{5\sqrt{18}{6} = \frac{15\sqrt{2}}{6}\)

= \(\frac{5\sqrt{2}}{2}\)


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