Question

Why root 2 is irrational no.

Answer 1

Let √2 be rational.
√2 = a/b
b√2 = a
Squaring both sides
2bsquare = asquare
Therefore, a is divisible by 2
Put a=2c
Then put a in the equation 2bsquare=asquare
2bsquare=4csquare
Dividing by 2
bsquare=2csquare
Therefore b is divisible by 2
Hence both a and b are divisible by 2.
Therefore a and b are not co-prime.
Therefore √2 is an irrational number.