# Prove that 3*2^1/2 is irrational

Solution::Let us assume ,to the contrary ,that $\\3\sqrt{2}$ is rational . then there exist co-prime positive integers a and b such that

$\\ 3\sqrt{2}=a/b\\ \\\Rightarrow \sqrt{2}=a/3b$

$\sqrt{2}$ is rational

the contradicts the fact that $\sqrt{2}$ is irrational . So ,our assumption is not correct

Hence ,$3\sqrt{2}$ is an irrational number.

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