Prove that 3+root 2 is a irrational number

1.	Prove that 3+root 2 is a irrational number
Answer» 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. HoPe It HeLpS yOu?? Let us consider that 3root2 is a rational number. It can be written in the form p/q (p and q are co primes)p/q = 3root2p/3q = root2Now,p/3q = integer/interger= rational numberBut, this contradicts the fact that root2 is irrational.Therefore, our assumption that 3root2 is rational is WRONG.Hence, 3root2 is an irrational number.

Discussion