Question: prove that root 3 + 2 root 5 is irrational?
Answer: So 3+2√5 = a/b where a,b are integers and are co primes and b is not equal to 0. ... => √5 is rational which is a contradiction since √5 is irrational. So our assumption that 2+3√5 is rational is wrong. So 2+3√5 is irrational.