Prove that 5−√3 is irrational
Let us assume the given number be rational and we will write the given number in p/q form
⇒5−√3=pq
⇒√3=5q−pq
We observe that LHS is irrational and RHS is rational, which is not possible.
This is contradiction.
Hence our assumption that given number is rational is false
⇒5−√3 is irrational