Question

prove that root 2 is irrational?​

Answer 1

Answer:

hey mate here is your answer

Sol: 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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Answer 2

so by contradiction

√3 is not a rational number

hence it is an irrational number

proved

just put 2,3,4,5,..... etc in the place of 3

you will get your required answer