Prove that 3 + 2√5 is irrational.

Let 3+2√5 is rational.
Therefore, we can find two co-prime integers a, b (b ≠ 0) such that
3+2√5 = a/b
2√5 = (a/b)-3
√5 = 1/2((a/b) – 3)
Since a andbare integers, 1/2((a/b) – 3) will also be rational and therefore, √5 is rational.
This contradicts the fact that √5 is irrational. Hence, our assumption that 3 + 2√5 is rational is false. Therefore, 3 +2√5 is irrational.

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