Question

prove that root 5 minus minus root 3 is irrational number​

Answer 1

Answer:

Suppose 5 +3√3 is rational . Let 5 +3√3 = r where r is a rational. ∴ (5 +3√3)2 = r2 ∴ 25+27 +30√3 = r2 ∴√3 = (r2 - 52) / 30 Now , LHS = √3 is an irrational number . RHS (r2 - 7) / 2 is a rational number . But rational number cannot be equal to an irrational. ∴our supposition is wrong. ∴ 5 + 3√3 is irrational .