Question

prove 7 root 5 is irrational

Answer 1

Let 7 root 5 be rational
7root5=a/b    {where a $ b are co-prime integers and b is not equal to 0}
root5=a/7b
since a $ b are integers, a/7b is rational, so root5 is also rational. But this contradicts the fact that root5 is irrational.
Hence 7root5 is irrational.

Answer 2

let assume that 7root 5be rational. for a rational number the formula is a/b
so.,7root5=a/b
root 5=a/b
because,7,a,andb are integers so therefore a/7b is a rational number
so ,root5 is rational number
this assumption that the fact root 5is irrational. so our assumption is not correct.