3. $[x]$ represents the greatest integer not greater than $x$, then the number of all real solutions to the equation $x^{2}-8[x]+7=0$ is ( ).
(A) 2
(B) 3
(C) 4
(D) 5
3.C.

Let $[x]=n$ (where $n$ is an integer), then $n \leqslant x4$. Therefore, $n=1,5,6,7$, and accordingly $x=1, \sqrt{33}, \sqrt{41}, 7$.