Let $$\alpha$$ denote the greatest integer $$\leq \alpha$$. Then $$\sqrt{1} + \sqrt{2} + \sqrt{3} + \ldots + \sqrt{120}$$ is equal to _____.

Find $$[\sqrt{1}] + [\sqrt{2}] + [\sqrt{3}] + \ldots + [\sqrt{120}]$$ where $$[x]$$ is the greatest integer function.

For $$n^2 \leq k < (n+1)^2$$, $$[\sqrt{k}] = n$$.

Count of integers k with $$[\sqrt{k}] = n$$: from $$n^2$$ to $$(n+1)^2 - 1$$, that's $$2n + 1$$ integers.

For $$n = 1$$: $$k = 1, 2, 3$$ (3 values), contribution = $$1 \times 3 = 3$$

For $$n = 2$$: $$k = 4, ..., 8$$ (5 values), contribution = $$2 \times 5 = 10$$

For $$n = 3$$: $$k = 9, ..., 15$$ (7 values), contribution = $$3 \times 7 = 21$$

For $$n = 4$$: $$k = 16, ..., 24$$ (9 values), contribution = $$4 \times 9 = 36$$

For $$n = 5$$: $$k = 25, ..., 35$$ (11 values), contribution = $$5 \times 11 = 55$$

For $$n = 6$$: $$k = 36, ..., 48$$ (13 values), contribution = $$6 \times 13 = 78$$

For $$n = 7$$: $$k = 49, ..., 63$$ (15 values), contribution = $$7 \times 15 = 105$$

For $$n = 8$$: $$k = 64, ..., 80$$ (17 values), contribution = $$8 \times 17 = 136$$

For $$n = 9$$: $$k = 81, ..., 99$$ (19 values), contribution = $$9 \times 19 = 171$$

For $$n = 10$$: $$k = 100, ..., 120$$ (21 values), contribution = $$10 \times 21 = 210$$

Total = $$3 + 10 + 21 + 36 + 55 + 78 + 105 + 136 + 171 + 210 = 825$$

The answer is $$\boxed{825}$$.