Show that 3√2 is irrational.
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 = ab⋅
Rearranging, we get √2 = a3b ⋅
Since 3, a and b are integers, a3b is rational, and so √2 is rational.
But this contradicts the fact that √2 is irrational.
So, we conclude that 3√2 is irrational.