Q. If P is a prime prove that √P is irrational.
Solution:-
           Let √P be rational
    √P = a/b  (a,b are co-prime),b is not equal to 0
    a = √Pb
    Squaring both sides
   a^2 = Pb^2.............(1)
  P divides a^2
  P divides a
  a = PR ( for some integer R)
  Put in (1)
  P^2R^2 = Pb^2
  PR^2 = b^2
  P  divides b^2
  P divides b
  b = PQ (for some integer Q)
  a = PR , b = PQ
But a,b are co-prime
This contradicts
Therefore,√P is irrational