Question

√5 is an irrational number
prove it

Answer 1

let √5 be an rational number
√5=a/b where a and b are co prime and b is not equal to 0
squaring both side 5=a^2/b^2
5b^2=a^2
therefore 5 divide a^2 , than 5 divide a



let a=5c for some integer c

5b^2=25c^2
b^2=5c^2


therefore a and b have atleast 5 as a common factor
But this contradiction the fact that a and b have no common factor other than 5
This contradiction has arisen because of our incorrect assumption that √5 is rational no.
so, i conclude that √5 is irrational no.

Answer 2

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