Question

prove that root 5 is irrational

Answer 1

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Answer 2

let √5 be a rational number
√5=a/b(a,b are co-prime integer and b≠0)
a=b√5
a²=5b²
------>5 is the factor of a²
------->5 is the factor of a
let. a=5c (c is some integer)
a²=25c²
5b²=25c²
b²=5c²
-------->5 is the factor of b²
--------->5 is the factor of b

therefore 5 is a common factor of a, b
but this contradiction the fact that a, b are co-primes

therefore √5 is irrational

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