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Perfect Squares 1 - 10000

?About This Table+
  • • The Perfect Square Tool above the table answers three kinds of questions
  • • "Is N a square?" tests any number: the tool reports the result and highlights the two nearest squares in the table
  • • "Square of N" computes N squared for any integer and jumps to that cell with its details open
  • • "Range" finds and highlights every perfect square that falls between two numbers you enter
  • • Each table cell shows the square root and the square for one of the 100 perfect squares from 1 to 10000
  • • Cells are color-coded by last digit — every perfect square ends in 0, 1, 4, 5, 6, or 9
  • • Hover any cell to see the gap to the next perfect square, which is always the next odd number
  • • Click a cell to open a details panel with prime factorizations, digit sum, last digit, and property tags
  • • The Patterns section has five filters: palindromic squares, squares ending in 25, Pythagorean triple members, prime-root squares, and square triangular numbers
  • • The Properties section explains four invariants: sum of odd numbers, odd divisor count, the 2n+1 gap, and the mod 4 rule
  • • The built-in quiz at the bottom lets you test your recall, with score persisting for the visit

Additional Resources

Root CalculatorSquare Root Visualizer

Perfect Square Tool

Every answer takes you to the table. Pick a question:

Last-digit color guide
ends in 0ends in 1ends in 4ends in 5ends in 6ends in 9

Every perfect square ends in one of these six digits. Numbers ending in 2, 3, 7, or 8 are never perfect squares.

1 — 100
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9
√100 = 10
121 — 400
√121 = 11
√144 = 12
√169 = 13
√196 = 14
√225 = 15
√256 = 16
√289 = 17
√324 = 18
√361 = 19
√400 = 20
441 — 900
√441 = 21
√484 = 22
√529 = 23
√576 = 24
√625 = 25
√676 = 26
√729 = 27
√784 = 28
√841 = 29
√900 = 30
961 — 1600
√961 = 31
√1024 = 32
√1089 = 33
√1156 = 34
√1225 = 35
√1296 = 36
√1369 = 37
√1444 = 38
√1521 = 39
√1600 = 40
1681 — 2500
√1681 = 41
√1764 = 42
√1849 = 43
√1936 = 44
√2025 = 45
√2116 = 46
√2209 = 47
√2304 = 48
√2401 = 49
√2500 = 50
2601 — 3600
√2601 = 51
√2704 = 52
√2809 = 53
√2916 = 54
√3025 = 55
√3136 = 56
√3249 = 57
√3364 = 58
√3481 = 59
√3600 = 60
3721 — 4900
√3721 = 61
√3844 = 62
√3969 = 63
√4096 = 64
√4225 = 65
√4356 = 66
√4489 = 67
√4624 = 68
√4761 = 69
√4900 = 70
5041 — 6400
√5041 = 71
√5184 = 72
√5329 = 73
√5476 = 74
√5625 = 75
√5776 = 76
√5929 = 77
√6084 = 78
√6241 = 79
√6400 = 80
6561 — 8100
√6561 = 81
√6724 = 82
√6889 = 83
√7056 = 84
√7225 = 85
√7396 = 86
√7569 = 87
√7744 = 88
√7921 = 89
√8100 = 90
8281 — 10000
√8281 = 91
√8464 = 92
√8649 = 93
√8836 = 94
√9025 = 95
√9216 = 96
√9409 = 97
√9604 = 98
√9801 = 99
√10000 = 100

Patterns to explore

Click a card to highlight every matching square in the table above.

↔

Palindromic squares

Squares that read the same forwards and backwards.

3 in tableClick to highlight
25

Squares ending in 25

Every square of a number ending in 5 ends in 25.

10 in tableClick to highlight
a²+b²

Pythagorean triple members

Squares whose root appears in an integer right triangle.

73 in tableClick to highlight
p

Squares with prime roots

Squares of prime numbers — their only divisors are 1, p, and p².

25 in tableClick to highlight
△□

Square triangular numbers

Both a perfect square and a triangular number (1+2+...+n).

3 in tableClick to highlight

Properties of perfect squares

Facts true of every perfect square — useful for spotting them and ruling them out.

Σ

Sum of consecutive odd numbers

n² equals the sum of the first n odd numbers. So 1+3+5+7+9 = 25 = 5².

d

Odd number of divisors

Perfect squares are the only positive integers with an odd count of divisors. 36 has 9 divisors: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Δ

Gap = next odd number

The difference between n² and (n+1)² is always 2n+1 — the next odd number.

10²=100, 11²=121, gap=21
mod

Mod 4 rule

Every perfect square is 0 or 1 mod 4 — never 2 or 3. Combined with the last-digit rule, this rejects most non-squares instantly.

1543 mod 4 = 3 → not a square
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