Prove that 3√2 is an irrational number

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 $Prove that 3 root 2 is$ ; where q ≠ 0 and let p, q are co-primes.

$Prove that 3 root 2 is$ 3√2 = $Prove that 3 root 2 is$ ………………. (i)

or it can be rearranged as √2 = $Prove that 3 root 2 is$

Since, 3, a and b are integers,

$Prove that 3 root 2 is$ 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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