# Prove that there is no rational number whose square is 2 :

“Prove that there is no rational number whose square is 2.” This type of proof is

(a) proof by contraposition

(b) direct proof

(c) proof by contradiction

(d) proof by counter-example

**Answer: (c) proof by contradiction **

**Solution:-**

**Given-
** √2 = m/n

where n and m are relatively prime, reduced to simplest form.

Clearly then, m cannot be even.

Square both sides:

2 = m² / n²

2 n² = m²

m² is even, so m must also be even.

Therefore assumption is false, and √2 cannot be expressed as a ratio of relatively prime integers so √2 is irrational, whose square is 2.