Question

prove that root 3is irrational number

Answer 1

let √3 be a rational number

√3 =a/b,where A and B are co primes and b is not equal to zero .

(by cross multiplication )

a=√3b
SBS
a square =√3b whole square
a square = 3 b square

root 3 is a factor of a and a square

a=3c
SBS
a square=3b square
9c square= 3b square

( here we cancel out 9 by 3 )

3c square = b square

under root 3 is a factor of b square and b


hence √3 is a factor of both a and b . but A and B are co primes hands as the position is wrong the √3 is an irrational number

Answer 2

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