Show that 3√2 is irrational. – InterviewSolution

1.

Show that 3√2 is irrational.

Answer»

Let us assume, to the contrary, that 3√2 is rational.

That is, we can find coprime a and b (b≠0) such that 3√2=a /b

Rearranging, we get √2=a/3b

Since 3, a and b are integers, a/3b is rational, and so √2 is rational.

But this contradicts the fact that √2 is irrational.

So, we conclude that 3√2 is irrational.

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