Chapter 1 Real Numbers Ex 1.3
Question 1.
Prove that √5 is irrational.
Solutions:
Question 2.
Prove that 3 + 2√5 is irrational.
Solutions:
Let us assume that 3 + 2√5 is rational.
∴ There exists co-prime integers a and b(b ≠ 0) such that
But this contradicts the fact that √5 is irrational.
This contradiction has arisen because of our incorrect assumption that 3 + 2√5 is rational. Hence, we conclude that 3 + 2√5 is irrational.
Question 3.
Prove that the following are irrationals.
Solutions:
