Use this Root Calculator to find square roots, cube roots, and general n-th roots in seconds. Enter any real number, choose the degree of the root, set your desired precision, and pick a rounding mode for a neatly presented answer.
What the Root Calculator Does
The Root Calculator computes the n-th root of a real number. That means it solves for a value r such that r raised to the power of n equals your input number. Common cases include the square root (n = 2) and the cube root (n = 3), but the calculator works for any integer degree n ? 1. For even degrees, the input must be non-negative to keep results in the real-number domain. For odd degrees, negative inputs are allowed and produce negative real roots.
How to Use the Root Calculator
- Enter your number (the radicand). For example, 144, 0.001, or -27.
- Choose the root degree n. Use 2 for square roots, 3 for cube roots, or any integer n ? 1 for general n-th roots.
- Set the number of decimal places to control precision.
- Select a rounding mode: Round (half up), Floor (toward ??), or Ceil (toward +?).
- Click Calculate Root to get the result instantly.
Examples
- Square root: If the radicand is 144 and n = 2, the result is 12.
- Cube root: If the radicand is -27 and n = 3, the result is -3 (odd roots allow negatives).
- General n-th root: For 32 with n = 5, the result is 2.
Why Use This Root Calculator?
Precision and control matter. This tool lets you choose decimal places and how the result is rounded, so your output fits your needs—whether you are preparing homework, engineering calculations, coding tasks, or quick checks for finance and science. The interface is streamlined and mobile-friendly, making it ideal for quick calculations on the go.
Rounding and Precision Explained
Precision sets how many decimal places are displayed. Rounding mode determines how the final value is adjusted:
- Round (half up): The conventional approach used in most contexts.
- Floor: Rounds down toward negative infinity, useful for conservative estimates.
- Ceil: Rounds up toward positive infinity, useful for upper bounds or capacity planning.
Mathematical Background
The n-th root of a non-negative number x is the number r such that rn = x. In real numbers, even-degree roots are defined only for x ? 0. Odd-degree roots are defined for all real x, and if x is negative, the root is negative. The calculator computes r = sign(x) · |x|1/n for odd n and checks domain restrictions for even n, returning a clear message if the requested root is not a real number.
Best Practices
- Use even degrees only with non-negative inputs for real results.
- For clean integers, try to recognize perfect powers to verify the result by mental math.
- Choose a precision that balances readability and accuracy—6 to 8 decimal places is usually enough.
- Pick a rounding mode that suits your use case: financial, scientific, or engineering contexts may differ.
Common Use Cases
Students use the Root Calculator for algebra and precalculus homework. Developers use it for algorithms that need n-th roots. Scientists and engineers apply it for scaling laws, signal processing, and unit conversions. Financial analysts may apply roots when working with compounded growth rates, such as computing the geometric average via n-th roots.
Get Started Now
Enter your values, choose the degree and precision, and click Calculate Root. In a moment, you will have an accurate, clearly rounded real-number result tailored to your needs.