Question

Prove the following -
(a) √2 is irrational


By long method and clear solution ​

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

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