Question

prove that root 5 + root 7 is irrational

Answer 1

We all know that √7 is irrational
Let us assume to the contrary that 5+√7 is rational
So,it can be written in the form a/b where a and b are co-primes,and b not equal to zero.
5+√7=a/b
√7=a-5b/b
Since a,b and 5 are integers, therefore the are rational
But this contradicts the fact that√7 is irrational
Hence our assumption is incorrect
Therefore 5+√7 is irrational