Note SpongeBob that
floor [ sqrt (1)] , floor [ sqrt (2)], floor [sqrt(3)] all = 1
And
floor [ sqrt (4)] through floor [sqrt (8)] = 2
And
floor [sqrt (9)] through floor [ sqrt (15)] = 3
And floor [ sqrt (16) )] = 4
So.....the sum is
3(1) + 5(2) + 7(3) + 4 =
3 + 10 + 21 + 4 =
38