Question

Prove that 3 + √5 is an irrational number.

Answer 1

Let us assume that 3 + √5 is a rational number. 

So, we can find co-prime integers ‘a’ and ‘b’ (b ≠ 0) such that

Since, a and b are integers, – 3 is a rational number and so √5 is a rational number. 

But this contradicts the fact that √5 is an irrational number. 

∴ Our assumption that 3 – √5 is a rational number is wrong. 

3 + √5 is an irrational number.