What are all of the square numbers up to 1000?

Answer 1

Squares of integers (and any other decimal number) can be easily found using a calculator.

The numbers that have squares less than 1000 are all numbers less than the square root of 1000, which is about 31.62 -- so integers between 1 and 31 have squares less than 1000. Note that each successive integer square is different from the preceding one by 2 more than the difference between the preceding pair (e.g. 262 - 252 = 51 and 252-242 = 49)

For any integer x, (x+1)2 = x2 + (x) + (x+1)

(1)2 = 1

(2)2 = 4

(3)2 = 9

(4)2 = 16

(5)2 = 25

(6)2 = 36

(7)2 = 49

(8)2 = 64

(9)2 = 81

(10)2 = 100

(11)2 = 121

(12)2 = 144

(13)2 = 169 (should memorize up to here)

(14)2 = 196

(15)2 = 225

(16)2 = 256

(17)2 = 289

(18)2 = 324

(19)2 = 361

(20)2 = 400

(21)2 = 441

(22)2 = 484

(23)2 = 529

(24)2 = 576

(25)2 = 625

(26)2 = 676

(27)2 = 729

(28)2 = 784

(29)2 = 841

(30)2 = 900

(31)2 = 961