A student writes the following argument: “

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems

Problem

18 = 9 \times 2

, so

\sqrt{18}=\sqrt{9}\times\sqrt{2}=3\times\sqrt{2}

. Since

3

and

\sqrt{2}

are integers,

\sqrt{18}

is rational.” (i) Identify the incorrect statement in the student’s argument. (ii) Provide a correct proof to establish whether

\sqrt{18}

is rational or irrational.