Question

Please tell me how to prove that root 2 is an irrational number descriptively step by step.

Answer 1

Given √2 is irrational number.
Let √2 = a / b wher a,b are integers b ≠ 0
we also suppose that a / b is written in the simplest form
Now √2 = a / b ⇒ 2 = a² / b² ⇒ 2b² = a²
∴ 2b² is divisible by 2
⇒ a² is divisible by 2
⇒ a is divisible by 2
∴ let a = 2c
a² = 4c² ⇒ 2b² = 4c² ⇒ b² = 2c²
∴ 2c² is divisible by 2
∴ b² is divisible by 2
∴ b is divisible by 2
∴a are b are divisible by 2 .
this contradicts our supposition that a/b is written in the simplest form
Hence our supposition is wrong
∴ √2 is irrational number.