Square $ABCD$ has side length 7. What is the length of the diagonal $AC?$ [asy] size(80); pair A = (0,0); pair B = ( 7,0); pair C = (7,7); pair D = (0,7); dot("$A$", A, SW); dot("$B$", B, SE); dot("$C$", C,
NE); dot("$D$", D, NW); draw(A--B--C--D--cycle); draw(A--C); label("$7$", (A+B)/2, S); [/asy]
