Question

Prove that
3 + √2is irrational​

Answer 1

Answer:

3+√2 = a/b ,where a and b are integers and b is not equal to zero .. therefore, √2 = (3b - a)/b is rational as a, b and 3 are integers.. But this contradicts the fact that √2 is irrational

Answer 2

Let us consider that 3√2 is a rational number. It can be written in the form p/q (p and q are co-primes). →p/q = 3√2. →p/3q = √2. Now, p/3q = integer/integer = rational number. But, this contradicts the fact that √2 is irrational. Therefore, our assumption that 3√2 is rational is WRONG. Hence, 3√2 is an irrational number.