Q) Prove that 3√2 is an irrational number.

Ans: Let us assume that 3√2 is a rational number

Then we can represent 3√2 as \frac{p}{q}; where q ≠ 0 and let p, q are co-primes.

\therefore  3√2 = \frac{p}{q} ………………. (i)

or it can be rearranged as √2 = \frac{p}{3q}

Since, 3, a and b are integers,

\therefore  \frac{p}{3q} is a rational number.

Hence, √2 is rational.

But it contradicts the fact that √2 is a irrational number;

Therefore, 3√2 is an irrational number………… Hence Proved !

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