Let’s assume √ab is equal to x.

Thus, √ab=x which implies ab=x^2.

Since √ab is a prime number, it can take values 2, 3, 5, 7, 11, 13,17 etc. Hence ab can take the values 4, 9, 25, 49, 121 etc.

But the product of a and b is even i.e. ab is even. Hence the only even number is the list of possible values for ab is 4.

Also, from b > 0 and a > 2b, we can say that a and b are positive.

From ab = 4, we can write a = 4/b which when substituted in a > 2b gives 4/b > 2b which implies 4 > 2b^2
So we can write it as 2 > b^2 which can be rewritten as b < √2≈1.414.

Therefore Quantity B is greater and the correct answer choice is B.