Prove that 3+2√ is irrational. [4 MARKS]
Concept : 1 Mark
Application : 1 Mark
procedure : 2 Marks
Let us assume, to the contrary, that 3+2√ is rational.
That is, we can find co-prime integers a and b(b≠0) such that 3+2√=ab
Since a and b are integers, we get a2b−32 is rational, and so a−3b2b=√ is rational.
But this contradicts the fact that √ is irrational.
This contradiction has arisen because of our incorrect assumption that 3+2√ is rational.
So, we conclude that 3+2√ is irrational.