# ?Prove that 3squre root 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

This 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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