Question

prove practically that root9 is irrational.

Answer 1

let as assume that √9 is a rational number.
such that, 
              √9 = a/b (where a and b are co - prime number)
             (squaring both sides)
             √9² = (a/b)²
              9 = a²/b²
             9b² = a²
              b² = a²/9
        ∴ 9 divides a² and
           9 also divides a
again,
a = 9m,
                  a = 9m
                  (squaring both sides)
                    a² = (9m)²
                    9b² = 81m²  (∵ 9b² = a²) 
                    9b²/81 = m²
                    b²/9 = m²
                   ∴ 9 divides b² and
                      9 also divides b
hence,
by this process , we say that 9 divides both a and b , which contradicts the fact.so, our assumption was wrong.
                        ∴ √5 is a irrational number