How to Use
Select Square Root for √n, Cube Root for ∛n, or Perfect Square/Cube Check to test a number.
Type any positive integer up to 1,000,000. Works for both perfect and non-perfect roots.
See the simplified radical form via prime factorisation, decimal value, and nearest perfect root — with full step-by-step working.
Perfect Squares (1² – 30²)
| n | n² | n | n² | n | n² |
|---|---|---|---|---|---|
| 1 | 1 | 11 | 121 | 21 | 441 |
| 2 | 4 | 12 | 144 | 22 | 484 |
| 3 | 9 | 13 | 169 | 23 | 529 |
| 4 | 16 | 14 | 196 | 24 | 576 |
| 5 | 25 | 15 | 225 | 25 | 625 |
| 6 | 36 | 16 | 256 | 26 | 676 |
| 7 | 49 | 17 | 289 | 27 | 729 |
| 8 | 64 | 18 | 324 | 28 | 784 |
| 9 | 81 | 19 | 361 | 29 | 841 |
| 10 | 100 | 20 | 400 | 30 | 900 |
Perfect Cubes (1³ – 20³)
| n | n³ | n | n³ | n | n³ |
|---|---|---|---|---|---|
| 1 | 1 | 8 | 512 | 15 | 3,375 |
| 2 | 8 | 9 | 729 | 16 | 4,096 |
| 3 | 27 | 10 | 1,000 | 17 | 4,913 |
| 4 | 64 | 11 | 1,331 | 18 | 5,832 |
| 5 | 125 | 12 | 1,728 | 19 | 6,859 |
| 6 | 216 | 13 | 2,197 | 20 | 8,000 |
| 7 | 343 | 14 | 2,744 |
Frequently Asked Questions
A perfect square is a number whose square root is a whole integer. E.g., 36 = 6², so √36 = 6. In prime factorization, every prime factor appears an even number of times (e.g., 36 = 2² × 3²).
72 = 2 × 2 × 2 × 3 × 3 = 2² × 3² × 2. Group pairs: √(2² × 3² × 2) = 2 × 3 × √2 = 6√2. Since one 2 is left unpaired inside, the result is irrational.
A perfect cube has a cube root that is a whole integer. E.g., 125 = 5³, so ∛125 = 5. In prime factorization, every prime appears in a multiple of 3 (e.g., 216 = 2³ × 3³).
54 = 2 × 3 × 3 × 3 = 2 × 3³. Group triples: ∛(3³ × 2) = 3 × ∛2 = 3∛2. One 2 remains inside, so the result is irrational.
For competitive exams (SSC, IBPS, CAT), memorise squares from 1² to 30² and cubes from 1³ to 10³. This covers 90% of simplification and square-root estimation questions you will encounter.