## prove that 3 √2 is an irrational number​

Question

prove that 3 √2 is an irrational number​

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2 months 2021-10-09T19:00:42+00:00 2 Answers 0 views 0

1. as √2 is an irrational number , we multiply 3 to √2 then it also becomes an irrational number

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let us assume that 3√2 is rational

Then we have two integers a and b such that:

3√2=a/b

√2=a/3b

a,b and 3 are integers,hence a/3b is rational

Since a/3b is rational

hence√2 is rational

But this contadicts the fact that √2 is irrational.

This contradiction has arisen due to our incorrect assumption that 3√2 is rational.

Hence 3√2 is irrational