Upper bounds known for length of side of the smallest square box in which one
may enclose  n  squares of side  1. (Decimals are approximate of course)
For more information including illustrations see 
  DS7: Erich Friedman, ``Packing Unit Squares in Squares''
  http://www.combinatorics.org/Surveys/index.html

 n         upper bound for  s(n)

 1 	   1 
 2--4 	   2 
 5 	   2 + (1/2) sqrt(2) = 2.7072 
 6--9 	   3 
 10 	   3 + (1/2) sqrt(2) = 3.7072 
 11 	   =3.8772 
 12--16    4 
 17 	   (7/3) + (5/3) sqrt(2) = 4.6904 
 18 	   (7/2) + (1/2) sqrt(7) = 4.8229 
 19 	   3 + (4/3) sqrt(2)  = 4.8857 
 20--25    5 
 26 	   (7/2) + (3/2) sqrt(2) = 5.6214 
 27 	   5 + (1/2) sqrt(2) = 5.7072 
 28 	   3 + 2 sqrt(2) = 5.8285 
 29 	   = 5.9665 
 30--36    6 
 37 	   = 6.6213 
 38 	   6 + (1/2) sqrt(2) = 6.7072 
 39 	   (11/2) + (1/2) sqrt(7) = 6.8229 
 40 	   4 + 2 sqrt(2) = 6.8285 
 41 	   2 + (7/2) sqrt(2) = 6.9498 
 42--49    7 
 50 	   = 7.6213 
 51--52    7 + (1/2) sqrt(2) = 7.7072 
 53 	   5 + 2 sqrt(2) = 7.8285 
 54 	   6 + (4/3) sqrt(2) = 7.8857 
 55--64    8 
 65 	   5 + (5/2) sqrt(2) = 8.5356 
 66 	   3 + 4 sqrt(2) = 8.6569 
 67 	   8 + (1/2) sqrt(2) = 8.7072 
 68 	   6 + 2 sqrt(2) = 8.8285 
 69 	   (5/2) + (9/2) sqrt(2) = 8.8640 
 70 	   (15/2) +  sqrt(2) = 8.9143 
 71--81    9 
 82 	   6 + (5/2) sqrt(2) = 9.5356 
 83 	   4 + 4 sqrt(2) = 9.6569 
 84 	   9 + (1/2) sqrt(2) = 9.7072 
 85 	   (11/2) + 3 sqrt(2) = 9.7427 
 86 	   (17/2) + (1/2) sqrt(7) = 9.8229 
 87 	   (14/3) + (11/3) sqrt(2) = 9.8522 
 88 	   (17/2) +  sqrt(2) = 9.9143 
 89 	   5 + (7/2) sqrt(2) = 9.9498 
 90--100   10