It follows from elementary properties if divisibility integer numbers, that



    an integer (positive) number is a square and is divisible by 7 if and only if 

    it is divisible by 49 and the quotient is a square of the integer number, too.



Therefore, we can re-formulate the problem's question in this equivalent form:

    how many are there integer numbers less or equal to    that are the squares ?



 = 41.14, and the squares lesser than this number are  1, 4, 9, 16, 25 and 36.


In total, their number is  6.


So, the answer to the problem's question is 6.