A binary operation ♦ is defined on the set R, of real numbers by \(a ♦ b = \frac{ab}{4}\). Find the value of \(\sqrt{2} ♦ \sqrt{6}\).
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Correct Answer: Option C
Explanation:
\(a ♦ b = \frac{ab}{4}\)
\(\sqrt{2} ♦ \sqrt{6} = \frac{\sqrt{2} \times \sqrt{6}}{4} = \frac{\sqrt{12}}{4}\)
= \(\frac{2\sqrt{3}}{4} \)
= \(\frac{\sqrt{3}}{2}\)
\(a ♦ b = \frac{ab}{4}\)
\(\sqrt{2} ♦ \sqrt{6} = \frac{\sqrt{2} \times \sqrt{6}}{4} = \frac{\sqrt{12}}{4}\)
= \(\frac{2\sqrt{3}}{4} \)
= \(\frac{\sqrt{3}}{2}\)