Squares, Cubes and Roots
Square roots are shown both in simplest radical form and as decimals.
Table
| n | n² | n³ | √n (exact) | √n | ∛n |
|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 4 | 8 | √2 | 1.414214 | 1.259921 |
| 3 | 9 | 27 | √3 | 1.732051 | 1.44225 |
| 4 | 16 | 64 | 2 | 2 | 1.587401 |
| 5 | 25 | 125 | √5 | 2.236068 | 1.709976 |
| 6 | 36 | 216 | √6 | 2.44949 | 1.817121 |
| 7 | 49 | 343 | √7 | 2.645751 | 1.912931 |
| 8 | 64 | 512 | 2√2 | 2.828427 | 2 |
| 9 | 81 | 729 | 3 | 3 | 2.080084 |
| 10 | 100 | 1,000 | √10 | 3.162278 | 2.154435 |
| 11 | 121 | 1,331 | √11 | 3.316625 | 2.22398 |
| 12 | 144 | 1,728 | 2√3 | 3.464102 | 2.289428 |
| 13 | 169 | 2,197 | √13 | 3.605551 | 2.351335 |
| 14 | 196 | 2,744 | √14 | 3.741657 | 2.410142 |
| 15 | 225 | 3,375 | √15 | 3.872983 | 2.466212 |
| 16 | 256 | 4,096 | 4 | 4 | 2.519842 |
| 17 | 289 | 4,913 | √17 | 4.123106 | 2.571282 |
| 18 | 324 | 5,832 | 3√2 | 4.242641 | 2.620741 |
| 19 | 361 | 6,859 | √19 | 4.358899 | 2.668402 |
| 20 | 400 | 8,000 | 2√5 | 4.472136 | 2.714418 |
| 21 | 441 | 9,261 | √21 | 4.582576 | 2.758924 |
| 22 | 484 | 10,648 | √22 | 4.690416 | 2.802039 |
| 23 | 529 | 12,167 | √23 | 4.795832 | 2.843867 |
| 24 | 576 | 13,824 | 2√6 | 4.898979 | 2.884499 |
| 25 | 625 | 15,625 | 5 | 5 | 2.924018 |
| 26 | 676 | 17,576 | √26 | 5.09902 | 2.962496 |
| 27 | 729 | 19,683 | 3√3 | 5.196152 | 3 |
| 28 | 784 | 21,952 | 2√7 | 5.291503 | 3.036589 |
| 29 | 841 | 24,389 | √29 | 5.385165 | 3.072317 |
| 30 | 900 | 27,000 | √30 | 5.477226 | 3.107233 |
Simplifying square roots
Take out the largest square factor: √72 = √(36 × 2) = 6√2. The square root calculator does this for any whole number.
Perfect squares to remember
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. Knowing these makes estimating other roots easy: √50 is just over 7, because 7² = 49.