Question

Can any one prove that root 2 is a irrational number....

Answer 1

let root 2 be a rational number
root 2=a/b a not equal to b
a nd b are co-prime
(root 2)sq=(a/b)sq
2/1=asq/bsq
by cross multiplication
asq=2bsq
2 is a factor of a
2 is also a factor of asq
asq=2csq
2bsq=(2c)sq
2bsq=4csq
cancle out 4 by 2
bsq=2csq
2 is a factor of b
2 is also a factor of bsq
therefore,2 is common factor of a nd b
This contradiction has arisen due to our incorrect assumption that root 2 is a rational number.
Hence root 2 is a irrational number.
HOPE THIS WILL BE HELPFUL FOR YOU...:)