Root Calculator
Calculate square roots, cube roots, and nth roots of any number with step-by-step explanations and adjustable precision.
How to Calculate Roots
- Enter the number you want to find the root of.
- Select the root degree: 2 for square root, 3 for cube root, or enter any custom degree.
- Click Calculate to get the result with adjustable decimal precision.
- Review the step-by-step breakdown showing the equivalent fractional exponent.
Referencia Rápida
| De | A |
|---|---|
| 2 + 3 | 5 |
| 12 × 12 | 144 |
| √144 | 12 |
| 2¹⁰ | 1,024 |
| π | 3.14159 |
| e | 2.71828 |
Casos de Uso
- •Geometry — calculate the side length of a square given its area using √(area).
- •Engineering — find the cube root of a volume to determine a container's edge length.
- •Programming — verify nth root computations when implementing math functions.
Fórmula
The nth root of x is x^(1/n). Square root: √x = x^(1/2). Cube root: ∛x = x^(1/3). For negative numbers, odd roots are real (e.g., ∛(−8) = −2), while even roots are not real.
Preguntas Frecuentes
What is the difference between a square root and a cube root?
A square root of x is a number that, when multiplied by itself, gives x (√9 = 3 because 3² = 9). A cube root is a number that, when cubed, gives x (∛27 = 3 because 3³ = 27).
Can you take the square root of a negative number?
Not in the real numbers. The square root of a negative number is an imaginary number (e.g., √(−1) = i). However, odd roots of negative numbers are real: ∛(−8) = −2.
How is the nth root related to exponents?
The nth root of x equals x raised to the power 1/n. So ⁿ√x = x^(1/n). This lets you compute any root using exponentiation.