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Rina says, “\(\sqrt{18}\) is rational because 18 is an integer.” Which option correctly identifies her error?

Answer and explanation

Correct answer: 18 is not a perfect square; \(\sqrt{18}=3\sqrt{2}\), which is irrational

18 is not a perfect square. \(\sqrt{18}=\sqrt{9\times2}=3\sqrt2\), and \(\sqrt2\) is irrational, so \(3\sqrt2\) is also irrational. Exam tip: factor the number into perfect-square factors before classifying its square root.

Related tags

Irrational NumbersSquare RootsPerfect SquaresNumber SystemsMisconception AnalysisMathematicsClass 9 Mcq

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