Property 7 There are no natural numbers `p and q` such that `p^2 = 2q^2`.

r, s, t are prime numbers and p, q are natural numbers such that LCM of p, q is r^(2)" "s^(4)" "t^(2) , then the number of ordered pairs (p,q) is

If p,q,r,s are natural numbers such that p>=q>=r If 2^(p)+2^(q)+2^(r)=2^(s) then

If p and q are positive real numbers such that p^(2)+q^(2)=1 then find the maximum value of (p+q)

if p and q are positive real numbers such that p^(2)+q^(2)=1 then find the maximum value of (p+q)

If p and q are positive real numbers such that p^2+q^2=1 , then the maximum value of p+q is

For any natural number p and q (i) p # q = p^3 + q^3 + 3 and p ** q = p^2 + q^2 + 2 and p $ q = |p - q| (ii) Max (p,q) = Maximum of (p,q) and Min (p and q) = Minimum of (p,q) The value of [(4 # 5) $ (14 ** 15)] is :

The sum of the factors of 9! Which are odd and are of the form 3m+2 , where m is a natural number is 8p+q , then the value of |p-q| is __________