Question: prove that sqrt(3) is an irrational number.hence show that 7+2 sqrt(3) is also an irrational number?
Answer: This can also be proved by the method of contradiction. ie , √3 is rational , which is a contradiction to the fact that √3 is irrational. This contradiction arises due to the fact the wrong assumption that 7 + 2√3 is rational. Hence it is proved that 7 + 2√3 is irrational.