The nth root of a number answers the question: “What number multiplied by itself n times equals the original value?” Our Nth Root Calculator lets you compute square roots, cube roots, fourth roots, and higher, quickly and with formatting options.
What does the calculator do?
- Accepts any number x and root index n.
- Returns the nth root as a decimal, with control over decimal places and scientific notation.
- Detects cases where no real root exists (e.g., even root of a negative).
- Provides a quick table of small integer roots of your chosen number.
Example: 81 with n=4 → ⁴√81 = 3.
Why are roots important?
- Algebra & Polynomials: nth roots appear in solving equations like xⁿ = a.
- Geometry & Scaling: square roots for areas, cube roots for volumes, higher roots in advanced topics.
- Science & Engineering: used in formula rearrangements, error analysis, and scale transformations.
Frequently Asked Questions
Q: What’s the difference between square, cube, and nth root?
Square root is n=2, cube root is n=3; nth root generalizes this to any integer n.
Q: Can I take even roots of negative numbers?
Not in real numbers. Even roots of negatives are complex. For odd roots, negative inputs are valid (e.g., ∛−8 = −2).
Q: Why does the calculator sometimes say “No real root”?
Because the root doesn’t exist in real numbers — try a complex number calculator for those cases.
Q: What are common uses of nth roots?
Simplifying radicals, solving exponential equations, and analysing growth/decay in science.