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A student claims that \(\frac{\sqrt{18}}{\sqrt{2}}\) must be irrational because both the numerator and denominator are irrational. What is the correct conclusion?

Answer and explanation

Correct answer: \(3\)

\(\frac{\sqrt{18}}{\sqrt{2}}=\sqrt{\frac{18}{2}}=\sqrt{9}=3\), which is rational. The quotient of two irrational numbers need not be irrational. Exam tip: combine the radicals before deciding the number type.

Related tags

Irrational NumbersSquare RootsRational NumbersNumber SystemsMisconception AnalysisMathematicsClass 9 Mcq

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