A binary operation * is defined on the set R of real numbers by a*b = \(\frac{\text{ab}}{4}\), find the value of \(\sqrt{2}\) * \(\sqrt{6}\)
a*b = \(\frac{\text{ab}}{4}\)
\(\sqrt{2}\) * \(\sqrt{6}\) = \(\frac{\text{ab}}{4}\)
\(\sqrt{2}\) * \(\sqrt{6}\) = \(\frac{\sqrt{2} \times \sqrt{6}}{4}\)
= \(\frac{\sqrt{12}}{4}\) = \(\frac{\sqrt{4} \times \sqrt{3}}{4}\) = \(\frac{2\sqrt{3}}{4}\) = \(\frac{\sqrt{3}}{2}\).
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