2022TrialShort answer

Q13 (b) (iii)

1 mark

Question

Using (i), prove that $\sqrt{18}$ is irrational.

Try the question before revealing the answer.

Solution

(iii) $\sqrt{18}=3\sqrt2$ .

If $\sqrt{18}$ is rational,

\frac{\sqrt{18}}{3}=\frac pq

\therefore \sqrt2=\frac p{3q},

which is rational.

But $\sqrt2$ is NOT rational.

$\therefore \sqrt{18}$ is irrational.

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Syllabus alignment

Proof

The Nature of ProofUse formal proof language, contradiction, counter-examples and rigorous arguments involving numbers and inequalities.

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