Instantly calculate any root, including square, cube, 4th, or 5th roots, with our free Nth Root Calculator. Get fast, accurate results with step-by-step solutions.
n = 2 (√), 3 (∛), 4 (⁴√), etc.
The number under the root symbol
Popular Examples – Click to Try:
Calculation Result
DEMO
Cube Root (3rd Root)
12
∛1728 = 12
Perfect Cube ✓
Root Index (n)
3
Radicand (Number)
1728
Result (ⁿ√)
12.000000
| Property | Value |
|---|---|
| Root Type | Cube Root (n = 3) |
| Original Number (Radicand) | 1728 |
| Nth Root Result | 12 |
| Verification | 12³ = 12 × 12 × 12 = 1728 ✓ |
| Exponent Form | 1728^(1/3) = 12 |
| Decimal Precision (10 places) | 12.0000000000 |
| Prime Factorization | 2⁶ × 3³ = (2² × 3)³ |
Nth Root Formula:
ⁿ√x = y where yⁿ = x
This means y multiplied by itself n times equals x
Alternative notation: ⁿ√x = x^(1/n)
Example: ∛1728 = 12, because 12³ = 12 × 12 × 12 = 1728
Even roots: For even n, the root of negative numbers yields complex results
Odd roots: For odd n, ⁿ√(-x) = -(ⁿ√x)
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