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Picturing
Square Numbers

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With Square Numbers
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Square Numbers

1 x 1 = 1    1 is a square number
2 x 2 = 4    4 is a square number
3 x 3 = 9    9 is a square number

4 x 4 = 16    16 is a square number
5 x 5 = 25    25 is a square number
6 x 6 = 36    36 is a square number
7 x 7 = 49    49 is a square number
8 x 8 = 64    64 is a square number
9 x 9 = 81    81 is a square number

10 x 10 = 100    100 is a square number

11 x 11 = 121    121 is a square number
12 x 12 = 144    144 is a square number
13 x 13 = 169    169 is a square number
14 x 14 = 196    196 is a square number
15 x 15 = 225    225 is a square number

and so on


QUESTION

Which of the following numbers is a square number?
200    300    400    500    600

Draw lines on a square
to divide into smaller squares

Lines Squares
2 4
4 9
6 16
8 25
10 36

A List Of The First 100 Square Numbers

1 x 1 = 1 21 x 21 = 441 41 x 41 = 1,681 61 x 61 = 3,721 81 x 81 = 6,561
2 x 2 = 4 22 x 22 = 484 42 x 42 = 1,764 62 x 62 = 3,844 82 x 82 = 6,724
3 x 3 = 9 23 x 23 = 529 43 x 43 = 1,849 63 x 63 = 3,969 83 x 83 = 6,889
4 x 4 = 16 24 x 24 = 576 44 x 44 = 1,936 64 x 64 = 4,096 84 x 84 = 7,056
5 x 5 = 25 25 x 25 = 625 45 x 45 = 2,025 65 x 65 = 4,225 85 x 85 = 7,225
         
6 x 6 = 36 26 x 26 = 676 46 x 46 = 2,116 66 x 66 = 4,356 86 x 86 = 7,396
7 x 7 = 49 27 x 27 = 729 47 x 47 = 2,209 67 x 67 = 4,489 87 x 87 = 7,569
8 x 8 = 64 28 x 28 = 784 48 x 48 = 2,304 68 x 68 = 4,624 88 x 88 = 7,744
9 x 9 = 81 29 x 29 = 841 49 x 49 = 2,401 69 x 69 = 4,761 89 x 89 = 7,921
10 x 10 = 100 30 x 30 = 900 50 x 50 = 2,500 70 x 70 = 4,900 90 x 90 = 8,100
         
11 x 11 = 121 31 x 31 = 961 51 x 51 = 2,601 71 x 71 = 5,041 91 x 91 = 8,281
12 x 12 = 144 32 x 32 = 1,024 52 x 52 = 2,704 72 x 72 = 5,184 92 x 92 = 8,464
13 x 13 = 169 33 x 33 = 1,089 53 x 53 = 2,809 73 x 73 = 5,329 93 x 93 = 8,649
14 x 14 = 196 34 x 34 = 1,156 54 x 54 = 2,916 74 x 74 = 5,476 94 x 94 = 8,836
15 x 15 = 225 35 x 35 = 1,225 55 x 55 = 3,025 75 x 75 = 5,625 95 x 95 = 9,025
         
16 x 16 = 256 36 x 36 = 1,296 56 x 56 = 3,136 76 x 76 = 5,776 96 x 96 = 9,216
17 x 17 = 289 37 x 37 = 1,369 57 x 57 = 3,249 77 x 77 = 5,929 97 x 97 = 9,409
18 x 18 = 324 38 x 38 = 1,444 58 x 58 = 3,364 78 x 78 = 6,084 98 x 98 = 9,604
19 x 19 = 361 39 x 39 = 1,521 59 x 59 = 3,481 79 x 79 = 6,241 99 x 99 = 9,801
20 x 20 = 400 40 x 40 = 1,600 60 x 60 = 3,600 80 x 80 = 6,400 100 x100 = 10,000

2 square numbers
that add to make
a square number

eg 9 + 16 = 25
eg 36 + 64 = 100
eg 81 + 144 = 225

Square numbers
that are
palindromic

eg 121
eg 484
eg 676

A square number
which is also
a cube number

eg 64
8 x 8 = 64
4 x 4 x 4 = 64

3 square numbers
that add to make
a square number

eg 4 + 9 + 36 = 49
eg 1 + 16 + 64 = 81
eg 16 + 25 + 400 = 441





EXTERNAL LINK Cambridge/Thesaurus/Square Number

EXTERNAL LINK Wolfram/MathWorld/Square Number





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