A binary operation ♦ is defined on the set R, of real numbers by \(a ♦ b = \frac{ab}{4}\). Find the value of \(\sqrt{2} ♦ \sqrt{6}\)

A.

\(\sqrt{3}\)

B.

\(\frac{3\sqrt{2}}{4}\)

C.

\(\frac{\sqrt{3}}{2}\)

D.

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

Correct answer is C

\(a ♦ b = \frac{ab}{4}\)

\(\sqrt{2} ♦ \sqrt{6} = \frac{\sqrt{2} \times \sqrt{6}}{4} = \frac{\sqrt{12}}{4}\)

= \(\frac{2\sqrt{3}}{4} \)

= \(\frac{\sqrt{3}}{2}\)