Root Calculator
Calculate square roots, cube roots, and nth roots of any number. This comprehensive root calculator supports both positive and negative numbers with precise decimal results.
Calculate Root
Result
Enter a number above to calculate its root
How to Use This Calculator
Select the type of root you want to calculate (square, cube, or nth root), enter your number, and optionally adjust the decimal precision. For nth roots, specify the root index. The calculator will instantly display the result along with verification.
How It Works
Square Root
The square root of a number x is a value that, when multiplied by itself, gives x. Formula: √x = y where y² = x
Cube Root
The cube root of a number x is a value that, when cubed, gives x. Formula: ∛x = y where y³ = x
Nth Root
The nth root of a number x is a value that, when raised to the power n, gives x. Formula: ⁿ√x = y where yⁿ = x
Example Calculations
Square Root
√16 = 4
√25 = 5
√2 ≈ 1.414
Cube Root
∛8 = 2
∛27 = 3
∛-8 = -2
Fourth Root
⁴√16 = 2
⁴√81 = 3
⁴√10 ≈ 1.778
Frequently Asked Questions
Can I calculate roots of negative numbers?
Yes, for odd roots (cube root, 5th root, etc.). Even roots of negative numbers result in complex numbers, which this calculator doesn't support.
What's the difference between rational and irrational roots?
Rational roots can be expressed as fractions (like √4 = 2), while irrational roots have infinite, non-repeating decimal expansions (like √2 ≈ 1.414...).
How accurate are the calculations?
The calculator uses JavaScript's built-in Math functions, providing accuracy up to about 15-17 significant digits for most calculations.