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Nth root calculator

Compute any root (square, cube, nth) of a number.

Related tools

All Algebra & equations tools →
Cube root calculatorCompute the cube root of a number, plus its cube.Primitive root calculatorFind the primitive roots modulo n — the generators g whose powers g¹, g², … run through every number coprime to n before repeating (order equal to φ(n)). Primitive roots exist only when n is 1, 2, 4, pᵏ or 2pᵏ for an odd prime p; the tool reports the smallest one, the exact count φ(φ(n)) and lists them. They are the backbone of discrete-logarithm cryptography and Diffie–Hellman key exchange.Square root calculatorCompute the square root of a number, plus its square.Digital Root CalculatorCompute the additive and multiplicative digital root of any number in base 2, 8, 10 or 16, with the full chain, the mod-9 shortcut and the persistence count.Rational Root Theorem CalculatorEvery ±p/q candidate, deduplicated and sorted, then actually tested — with the real roots, their multiplicity and the depressed polynomial left after dividing them out.Root Mean Square CalculatorRMS shown next to the plain mean, because on signed data the mean collapses to nearly zero while the RMS holds the magnitude that actually matters. Also gives the crest factor, the sum of squares and each value's share of it.Quadratic Formula CalculatorSolve ax² + bx + c = 0: get the discriminant, both roots and the nature of the solutions.Absolute Value Equation SolverSolve absolute-value equations like |x+3| = 5, 3|x+2| = 12 or |x+1| = |x−3| with step-by-step case analysis and exact solutions.

The Nth root calculator turns Number, Root (n) into Result, instantly and for free. For instance, with Number = 64 and Root (n) = 3 it returns Result = 4.

How to use it

  1. Enter your values: Number, Root (n).
  2. Read the result instantly: Result.

Frequently asked questions

How does the Nth root calculator work?

It takes Number and Root (n) and derives Result from them. The calculation is live as you type, so the result updates on every change.

Which values does the calculator ask for?

2 values: Number and Root (n). Nothing else is required — no account, no file upload.

What does a typical calculation look like?

With Number = 64 and Root (n) = 3, the calculator returns Result = 4. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

How much does the result change with different inputs?

It moves a lot. Using Number = 128 and Root (n) = 6 instead, Result goes from 4 to 2.245 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to Number = 32 and Root (n) = 2, Result comes out at 5.657. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

What is the difference between the Nth root calculator and the Cube root calculator?

This one returns Result; the Cube root calculator returns Cube root and Cube (n³). That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Primitive root calculator is the closest one after this: Find the primitive roots modulo n — the generators g whose powers g¹, g², … run through every number coprime to n before repeating (order equal to φ(n)). Primitive roots exist only when n is 1, 2, 4, pᵏ or 2pᵏ for an odd prime p; the tool reports the smallest one, the exact count φ(φ(n)) and lists them. They are the backbone of discrete-logarithm cryptography and Diffie–Hellman key exchange.

What else is worth having open alongside it?

Square root calculator and Digital Root Calculator — they come up in the same task often enough to be worth a second tab.

Further reading

All guides →
How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.