Calculate square roots, cube roots, and nth roots of any number. Shows simplified radical form.
Perfect square ✓
| Input | 144 |
| Result | 12 |
| Simplified Radical | 12 |
| Is Perfect Root | Yes ✓ |
| Verify (result²) | 144 |
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√n = n^(1/2)
ⁿ√n = n^(1/n)
Simplified: √72 = √(36×2) = 6√2
The square root of n is the number that, multiplied by itself, gives n. √9 = 3 because 3 × 3 = 9.
Numbers whose square root is a whole number: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225...
The cube root of n is the number that, cubed, gives n. ∛8 = 2 because 2³ = 8.
Architecture, physics, finance (standard deviation), geometry (diagonal of a square = side × √2).
Calculations are for educational purposes only. Consult a qualified financial advisor for personalized advice.