Find any root and its simplified radical form.
Pull out perfect squares: √72 = 8.4852813742386 — written 6√2, since 72 = 36 × 2.
A root undoes a power: the square root of 81 is 9 because 9² = 81. This calculator finds square roots, cube roots and any nth root (degree 2 to 100) of any number, shows the simplified radical form of integers (for example √72 = 6√2) and gives complex answers for even roots of negative numbers, such as √−4 = ±2i.
A root is a fractional power: ⁿ√x = x^(1/n) — see the Exponent Calculator. Related: Quadratic Formula Calculator, Prime Factorization Calculator, Pythagorean Theorem Calculator and the Scientific Calculator.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| Principal root | 8.4852813742386 |
| Simplified radical form | 6 × √2 |
| Check: root ^ 2 | 72 |
| Root | Result |
|---|---|
| √72 | 8.4852813742386 |
| √81 | 9 |
| ∛27 | 3 |
| ∛54 | 3.7797631496846 |
| √−4 | ±2i |
| n | n² | n³ | √n | ∛n |
|---|---|---|---|---|
| 1 | 1 | 1 | 1.0000 | 1.0000 |
| 2 | 4 | 8 | 1.4142 | 1.2599 |
| 3 | 9 | 27 | 1.7321 | 1.4422 |
| 4 | 16 | 64 | 2.0000 | 1.5874 |
| 5 | 25 | 125 | 2.2361 | 1.7100 |
| 6 | 36 | 216 | 2.4495 | 1.8171 |
| 7 | 49 | 343 | 2.6458 | 1.9129 |
| 8 | 64 | 512 | 2.8284 | 2.0000 |
| 9 | 81 | 729 | 3.0000 | 2.0801 |
| 10 | 100 | 1000 | 3.1623 | 2.1544 |
| 11 | 121 | 1331 | 3.3166 | 2.2240 |
| 12 | 144 | 1728 | 3.4641 | 2.2894 |
| 13 | 169 | 2197 | 3.6056 | 2.3513 |
| 14 | 196 | 2744 | 3.7417 | 2.4101 |
| 15 | 225 | 3375 | 3.8730 | 2.4662 |
A number that, multiplied by itself, gives the original number. √49 = 7.
Factor out the largest perfect square: √72 = √(36 × 2) = 6√2.
A real negative number: ∛(−27) = −3.
There is no real answer; the result is imaginary: √−4 = 2i (and −2i).
Raise the number to the power 1/n, or use this calculator: ⁴√81 = 3.
A whole number whose square root is a whole number, like 1, 4, 9, 16, 25.
It uses the standard method: ⁿ√x = x^(1/n) √(a² × b) = a√b The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
