The difference is 1

We used the following program to get the answer

for i in range(200,8400):

 z=i+i**0.5

 if (z%1==0):

     print (z)

In the output you will not get 7800 but you will get all the rest numbers

Hence the answer is 7800

Ans: \ 7800 )

The answer is an integer, this means that $a$ is a perfect square number.

You may note that $(a + \sqrt{a}) = \sqrt{a}(1 +\sqrt{a})$ , which is the product of two consecutive numbers. The only number that doesn't satisfy the equation is $8700$ .