Question

Prove that √5 is an irrational number. Hence, show that 4 + 2√5 is also an irrational number.

Answer 1

Answer:

Let √5 be a rational number. √5 = a / b , (a, b are co-primes and b ≠ 0) or, a = b√5 On squaring both the sides, we get or, 2- a = √5 2 - a is rational But √5 is not rational :. 2 - √5 is irrational.