4. (1990, 1st "Hope Cup" Mathematics Competition) Find the value of $[\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+\cdots+[\sqrt{1989 \cdot 1990}]+$ $[-\sqrt{1}]+[-\sqrt{2}]+[-\sqrt{3}]+\cdots+[-\sqrt{1989 \cdot 1990}]$.
4. When $x$ is a perfect square,
$$
[\sqrt{x}]+[-\sqrt{x}]=0 ;
$$

When $x$ is not a perfect square,
$$
[\sqrt{x}]+[-\sqrt{x}]=-1 \text {. }
$$

It is known that there are $1989 \cdot 1990$ pairs of numbers, among which there are 1989 pairs of perfect squares, and $1989^{2}$ pairs of non-perfect squares, so their sum is
$$
--1989^{2}=-3956121 .
$$