Prove that root 2 a irrational number

1.	Prove that root 2 a irrational number
Answer» Given √2 is irrational number.Let √2 = a / b wher a,b are integers b ≠ 0we also suppose that a / b is written in the simplest formNow √2 = a / b⇒ 2 = a2 / b2\xa0⇒ 2b2 = a2∴ 2b2 is divisible by 2⇒ a2 is divisible by 2 ⇒ a is divisible by 2 ∴ let a = 2ca2 = 4c2⇒ 2b2 = 4c2⇒\xa0b2 = 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 formHence our supposition is wrong∴ √2 is irrational number.

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