The first 100 square numbers are 12, 22, 32, ..., 1002 which are:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3136, 3249, 3364, 3481, 3600, 3721, 3844, 3969, 4096, 4225, 4356, 4489, 4624, 4761, 4900, 5041, 5184, 5329, 5476, 5625, 5776, 5929, 6084, 6241, 6400, 6561, 6724, 6889, 7056, 7225, 7396, 7569, 7744, 7921, 8100, 8281, 8464, 8649, 8836, 9025, 9216, 9409, 9604, 9801, 10000
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Square: 1,4,9,16,25,36,49,64,81,and 100 cube: sorry?!?
There are 10 square numbers
Both 25 and 4 are factors of 100 and are square numbers, 25 is 52 and 4 is 22. 100 and 1 are also factors of 100, and are also square numbers: 1 is 12 and 100 is 102.
There are 10 square numbers from 1 to 100, so the median is the mean average of the middle two - the 5th and 6th square numbers = (25 + 36) ÷ 2 = 30.5
All numbers are square numbers, for example, the square root of 2 squared is 2. If you mean perfect squares, here's a list: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100