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By simplifying \((\sqrt{3}+\sqrt{2}) * (\sqrt{3}+\sqrt{2})\), we get __________(a) 5 + 4√6(b) 5 + 2√6(c) 1(d) 5This question was posed to me in an international level competition.The origin of the question is Representing Real Numbers on the Number Line & Real Numbers Operations topic in division Number Systems of Mathematics – Class 9

Answer»

Correct option is (b) 5 + 2√6

Explanation: We KNOW that \((\sqrt{a}+\sqrt{b}) * (\sqrt{a}+\sqrt{b}) = a + 2\sqrt{a}\sqrt{b} + b.\)

By applying that rule here, we GET \((\sqrt{3}+\sqrt{2}) * (\sqrt{3}+\sqrt{2}) = 3 + 2\sqrt{3}\sqrt{2} + 2

= 5 + 2\sqrt{6}\) SINCE \(\sqrt{a}\sqrt{b} = \sqrt{(ab)}\),

\(\sqrt{3}\sqrt{2} = \sqrt{(3*2)} = \sqrt{6}\).


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