WAEC - Further Mathematics (2006 - No. 4)
A binary operation ♦ is defined on the set R, of real numbers by \(a ♦ b = \frac{ab}{4}\). Find the value of \(\sqrt{2} ♦ \sqrt{6}\).
\(\sqrt{3}\)
\(\frac{3\sqrt{2}}{4}\)
\(\frac{\sqrt{3}}{2}\)
\(\frac{\sqrt{2}}{2}\)
Explanation
\(a ♦ b = \frac{ab}{4}\)
\(\sqrt{2} ♦ \sqrt{6} = \frac{\sqrt{2} \times \sqrt{6}}{4} = \frac{\sqrt{12}}{4}\)
= \(\frac{2\sqrt{3}}{4} \)
= \(\frac{\sqrt{3}}{2}\)
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