Computed, not transcribed
Squares and cubes are exact integers; the two root columns are rounded to six decimal places and every value is produced by the shared MathOps helpers rather than typed in.
Squares, Cubes and Roots Table
n, n², n³, √n and ∛n for every integer from 1 to 100 — with the perfect squares and perfect cubes marked.
Rows
1 – 100
Perfect squares
10
Perfect cubes
4
Decimal places
6
Between 1 and 100 there are 10 perfect squares and 4 perfect cubes; the roots of every other number are irrational and rounded here to 6 places.
Verified
Squares, Cubes and Roots Table — in full
100 of 100 rows
| n | n² | n³ | √n | ∛n |
|---|---|---|---|---|
| 1 | 1 | 1 | 1.000000 | 1.000000 |
| 2 | 4 | 8 | 1.414214 | 1.259921 |
| 3 | 9 | 27 | 1.732051 | 1.442250 |
| 4 | 16 | 64 | 2.000000 | 1.587401 |
| 5 | 25 | 125 | 2.236068 | 1.709976 |
| 6 | 36 | 216 | 2.449490 | 1.817121 |
| 7 | 49 | 343 | 2.645751 | 1.912931 |
| 8 | 64 | 512 | 2.828427 | 2.000000 |
| 9 | 81 | 729 | 3.000000 | 2.080084 |
| 10 | 100 | 1,000 | 3.162278 | 2.154435 |
| 11 | 121 | 1,331 | 3.316625 | 2.223980 |
| 12 | 144 | 1,728 | 3.464102 | 2.289428 |
| 13 | 169 | 2,197 | 3.605551 | 2.351335 |
| 14 | 196 | 2,744 | 3.741657 | 2.410142 |
| 15 | 225 | 3,375 | 3.872983 | 2.466212 |
| 16 | 256 | 4,096 | 4.000000 | 2.519842 |
| 17 | 289 | 4,913 | 4.123106 | 2.571282 |
| 18 | 324 | 5,832 | 4.242641 | 2.620741 |
| 19 | 361 | 6,859 | 4.358899 | 2.668402 |
| 20 | 400 | 8,000 | 4.472136 | 2.714418 |
| 21 | 441 | 9,261 | 4.582576 | 2.758924 |
| 22 | 484 | 10,648 | 4.690416 | 2.802039 |
| 23 | 529 | 12,167 | 4.795832 | 2.843867 |
| 24 | 576 | 13,824 | 4.898979 | 2.884499 |
| 25 | 625 | 15,625 | 5.000000 | 2.924018 |
| 26 | 676 | 17,576 | 5.099020 | 2.962496 |
| 27 | 729 | 19,683 | 5.196152 | 3.000000 |
| 28 | 784 | 21,952 | 5.291503 | 3.036589 |
| 29 | 841 | 24,389 | 5.385165 | 3.072317 |
| 30 | 900 | 27,000 | 5.477226 | 3.107233 |
| 31 | 961 | 29,791 | 5.567764 | 3.141381 |
| 32 | 1,024 | 32,768 | 5.656854 | 3.174802 |
| 33 | 1,089 | 35,937 | 5.744563 | 3.207534 |
| 34 | 1,156 | 39,304 | 5.830952 | 3.239612 |
| 35 | 1,225 | 42,875 | 5.916080 | 3.271066 |
| 36 | 1,296 | 46,656 | 6.000000 | 3.301927 |
| 37 | 1,369 | 50,653 | 6.082763 | 3.332222 |
| 38 | 1,444 | 54,872 | 6.164414 | 3.361975 |
| 39 | 1,521 | 59,319 | 6.244998 | 3.391211 |
| 40 | 1,600 | 64,000 | 6.324555 | 3.419952 |
| 41 | 1,681 | 68,921 | 6.403124 | 3.448217 |
| 42 | 1,764 | 74,088 | 6.480741 | 3.476027 |
| 43 | 1,849 | 79,507 | 6.557439 | 3.503398 |
| 44 | 1,936 | 85,184 | 6.633250 | 3.530348 |
| 45 | 2,025 | 91,125 | 6.708204 | 3.556893 |
| 46 | 2,116 | 97,336 | 6.782330 | 3.583048 |
| 47 | 2,209 | 103,823 | 6.855655 | 3.608826 |
| 48 | 2,304 | 110,592 | 6.928203 | 3.634241 |
| 49 | 2,401 | 117,649 | 7.000000 | 3.659306 |
| 50 | 2,500 | 125,000 | 7.071068 | 3.684031 |
| 51 | 2,601 | 132,651 | 7.141428 | 3.708430 |
| 52 | 2,704 | 140,608 | 7.211103 | 3.732511 |
| 53 | 2,809 | 148,877 | 7.280110 | 3.756286 |
| 54 | 2,916 | 157,464 | 7.348469 | 3.779763 |
| 55 | 3,025 | 166,375 | 7.416198 | 3.802952 |
| 56 | 3,136 | 175,616 | 7.483315 | 3.825862 |
| 57 | 3,249 | 185,193 | 7.549834 | 3.848501 |
| 58 | 3,364 | 195,112 | 7.615773 | 3.870877 |
| 59 | 3,481 | 205,379 | 7.681146 | 3.892996 |
| 60 | 3,600 | 216,000 | 7.745967 | 3.914868 |
| 61 | 3,721 | 226,981 | 7.810250 | 3.936497 |
| 62 | 3,844 | 238,328 | 7.874008 | 3.957892 |
| 63 | 3,969 | 250,047 | 7.937254 | 3.979057 |
| 64 | 4,096 | 262,144 | 8.000000 | 4.000000 |
| 65 | 4,225 | 274,625 | 8.062258 | 4.020726 |
| 66 | 4,356 | 287,496 | 8.124038 | 4.041240 |
| 67 | 4,489 | 300,763 | 8.185353 | 4.061548 |
| 68 | 4,624 | 314,432 | 8.246211 | 4.081655 |
| 69 | 4,761 | 328,509 | 8.306624 | 4.101566 |
| 70 | 4,900 | 343,000 | 8.366600 | 4.121285 |
| 71 | 5,041 | 357,911 | 8.426150 | 4.140818 |
| 72 | 5,184 | 373,248 | 8.485281 | 4.160168 |
| 73 | 5,329 | 389,017 | 8.544004 | 4.179339 |
| 74 | 5,476 | 405,224 | 8.602325 | 4.198336 |
| 75 | 5,625 | 421,875 | 8.660254 | 4.217163 |
| 76 | 5,776 | 438,976 | 8.717798 | 4.235824 |
| 77 | 5,929 | 456,533 | 8.774964 | 4.254321 |
| 78 | 6,084 | 474,552 | 8.831761 | 4.272659 |
| 79 | 6,241 | 493,039 | 8.888194 | 4.290840 |
| 80 | 6,400 | 512,000 | 8.944272 | 4.308869 |
| 81 | 6,561 | 531,441 | 9.000000 | 4.326749 |
| 82 | 6,724 | 551,368 | 9.055385 | 4.344481 |
| 83 | 6,889 | 571,787 | 9.110434 | 4.362071 |
| 84 | 7,056 | 592,704 | 9.165151 | 4.379519 |
| 85 | 7,225 | 614,125 | 9.219544 | 4.396830 |
| 86 | 7,396 | 636,056 | 9.273618 | 4.414005 |
| 87 | 7,569 | 658,503 | 9.327379 | 4.431048 |
| 88 | 7,744 | 681,472 | 9.380832 | 4.447960 |
| 89 | 7,921 | 704,969 | 9.433981 | 4.464745 |
| 90 | 8,100 | 729,000 | 9.486833 | 4.481405 |
| 91 | 8,281 | 753,571 | 9.539392 | 4.497941 |
| 92 | 8,464 | 778,688 | 9.591663 | 4.514357 |
| 93 | 8,649 | 804,357 | 9.643651 | 4.530655 |
| 94 | 8,836 | 830,584 | 9.695360 | 4.546836 |
| 95 | 9,025 | 857,375 | 9.746794 | 4.562903 |
| 96 | 9,216 | 884,736 | 9.797959 | 4.578857 |
| 97 | 9,409 | 912,673 | 9.848858 | 4.594701 |
| 98 | 9,604 | 941,192 | 9.899495 | 4.610436 |
| 99 | 9,801 | 970,299 | 9.949874 | 4.626065 |
| 100 | 10,000 | 1,000,000 | 10.000000 | 4.641589 |
How to read this table
Read the row for your number n. n² and n³ are exact integers; √n and ∛n are rounded to six decimal places.
A highlighted row means n is a perfect square or cube. The root column then shows a whole number rather than a rounded decimal.
The table works in both directions: to find the square root of 64, look for 64 in the n² column — its row is n = 8.
n² against n³
- n²
- n³
Hover the chart to read the precise values.
On a logarithmic axis both become straight lines — the cube line rises exactly one and a half times as steeply as the square line.
Gap between consecutive squares
Hover the chart to read the precise values.
The gaps are exactly the odd numbers 3, 5, 7, 9 … — because (n + 1)² − n² always equals 2n + 1.
Perfect squares per block of ten
Hover the chart to read the precise values.
Perfect squares thin out as numbers grow, because the gap between them increases linearly.
How this table is built
Sources & verification
This table needs no external source: every value follows directly from the arithmetic and is recomputed each time the page is built.
Last checked against the sources on August 6, 2026.
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Frequently asked questions
Which perfect squares are there up to 100?
There are 10: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Their roots are the whole numbers 1 to 10.
Which perfect cubes are there up to 100?
Four: 1, 8, 27, 64. The number 1 is both a square and a cube, because 1 raised to any power is 1 again.
Why are the gaps between squares the odd numbers?
Because (n + 1)² − n² simplifies to 2n + 1, and 2n + 1 is odd for every whole n. That is also why every square is the sum of the odd numbers up to its own gap.
Why are most of the roots rounded?
The root of a number that is not a perfect square is irrational — it has infinitely many non-repeating decimals. This table shows 6 of them, which is enough for any everyday calculation.
How do square and cube roots differ?
The square root asks which number multiplied by itself gives n; the cube root asks which number multiplied by itself three times gives n. That is why ∛n grows much more slowly than √n.
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