Question

Prove that 1/√3 is irriational number

Answer 1

Answer:

3 will be a factor of both p and q which contradicts are statement. that they both have a hcf of 1. so we make a conclusion that although 2 is rational but √3 is irrational. let us assume to the contrary that 1/√3 is rational number .

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Answer 2

Answer:

let 1/√3 is rational number

therefore we can find two co-prime integers a, b such that

=> 1/√3 = a/b

=> √3 = b/a

a/b is rational as a and b are integers

therefore √3 is rational which contradict to the fact that √3 is irrational

hence our assumption is false and 1/√3 is irrational