Math & Engineering
Root Calculator
Calculate any root (square root, cube root, or nth root) of a number
Reviewed by the calculator.uk.com Team · Last reviewed 19 June 2026 · Our methodology
Enter a number and root value to calculate
Related to Root Calculator
The root calculator finds the nth root of any number using advanced mathematical algorithms. A root (or radical) is the inverse operation of exponentiation. When we say we want to find the nth root of a number, we're looking for what number, when raised to the power of n, gives us our original number.
Mathematical Formula
For a number x and root n, we calculate: y = ∛x = x^(1/n) This means that y^n = x
The calculator handles both positive and negative numbers appropriately. For negative numbers, it considers whether the root is odd or even. Odd roots of negative numbers exist and are negative, while even roots of negative numbers are undefined in the real number system.
The calculator provides the exact nth root of your input number. The result is displayed with up to 6 decimal places for precision, with trailing zeros removed for clarity. Here's how to interpret different scenarios:
Common Root Types
• Square Root (n=2): The most common root, written as √x
• Cube Root (n=3): Written as ∛x
• Fourth Root (n=4): The root that, when taken to the fourth power, equals the input
• Higher Roots: Follow the same pattern, becoming more specialized
1. What is a root in mathematics?
A root is a value that, when multiplied by itself a certain number of times (as specified by the root degree), produces the given number. For example, 2 is the square root of 4 because 2 × 2 = 4.
2. Can I find roots of negative numbers?
Yes, but with limitations. Odd roots (3rd, 5th, etc.) of negative numbers exist and are negative. Even roots (2nd, 4th, etc.) of negative numbers are undefined in the real number system.
3. Why do some results have decimal places?
Most root calculations result in irrational numbers that cannot be expressed as simple fractions. We display these results with up to 6 decimal places for practical purposes while maintaining accuracy.
4. What is the difference between square root and cube root?
A square root (n=2) is a number that, when multiplied by itself, gives the original number. A cube root (n=3) is a number that, when multiplied by itself twice, gives the original number. For example, the square root of 9 is 3 (3×3=9), and the cube root of 27 is 3 (3×3×3=27).
5. What is the scientific source for this calculator?
Roots are the inverse of exponentiation: this calculator computes the nth root of x using the identity x^(1/n), evaluated with JavaScript's Math.pow(). For negative inputs, it follows the standard algebraic convention that odd roots exist and are negative, while even roots are undefined in the real number system.