Example 1. Calculate: $\sqrt{31 \cdot 30 \cdot 29 \cdot 28+1}$. (7th American Invitational Mathematics Examination)
```
\begin{array}{l} 
\because \sqrt{ }(x+1) x(x-1)(x-2)+1 \\
= \sqrt{ }\left(x^{2}-x-2\right)\left(x^{2}-x\right)+1 \\
= \sqrt{ }\left(x^{2}-x-1\right)^{2} \\
=\left|x^{2}-x-1\right| . \\
\therefore \text { when } x=30 \text {, the original expression }=\left|30^{2}-30-1\right| \\
=869 .
\end{array}
```