Let us assume on the contrary that 1/√2 is rational
then, 1/√2 = p/q (whare p and q are co prime integers)
√2 =q/p

As p and q are co prime integers then q/p is rational
then √2 is also rational
But this contradicts the fact that √2 is irrational.
This contradiction has arised due to our wrong assumption
Therefore 1/√2 is irrational

Proving Irrationality of √2:
Understanding Rational and Irrational Numbers:
- Rational numbers can be expressed as a ratio of two integers.
- Irrational numbers cannot be expressed as a simple fraction and have non-repeating decimal expansions.

Proof by Contradiction:
Assume √2 is rational:
- If √2 is rational, it can be expressed as a/b where a and b are integers with no common factors.
- Therefore, (√2)^2 = 2 = a^2/b^2.
- This implies that 2b^2 = a^2. Since a^2 is even, a must be even.
- If a is even, let a = 2k for some integer k. Substituting back, we get 2b^2 = (2k)^2 = 4k^2.
- Simplifying, b^2 = 2k^2. This means b^2 is also even, hence b must be even.
Contradiction:
- If both a and b are even, they have a common factor of 2. This contradicts our assumption that a and b have no common factors.
- Therefore, our initial assumption that √2 is rational must be false.

Conclusion:
- Since our assumption leads to a contradiction, we can conclude that √2 is irrational. It cannot be expressed as a simple fraction and has a non-repeating decimal expansion.