Nth Root Calculator
Calculate the nth root of any real number to up to 100 decimal places, with automatic exact-root detection and a verification step showing the rounded result raised back to the nth power.
Input
Digits shown after the decimal point (up to 100).
Output
The rounded result raised back to the nth power, compared to the original number.
Guides
The Nth Root Calculator finds the nth root of any real number — square roots, cube roots, or any degree up to 100 — computed to up to 100 decimal places of precision. It also tells you whether the result is exact and shows a verification step, raising the rounded root back to the nth power so you can confirm it against the original number.
It's built for students who need more precision than a pocket calculator gives, and for anyone who wants to double-check whether a root is a clean integer or an endless irrational decimal.
How to use it
- Enter the Number you want to take the root of — any real number, positive or negative, whole or decimal (e.g.
27,-8,3.14159). - Enter the Root degree (n) —
2for a square root,3for a cube root, or any whole number up to 100. - Adjust Decimal places (0–100) for how much precision you need.
- Read the Result, whether it's an Exact root, and the Verification line showing the rounded result raised back to the nth power.
For example, entering 27 with degree 3 returns 3 exactly (27 is a perfect cube), while 2 with degree 2 returns 1.41421356... and is flagged as irrational.
What is an nth root?
The nth root of a number x is a value r such that r^n = x. A square root (n = 2) undoes squaring; a cube root (n = 3) undoes cubing. An even-degree root of a negative number has no real result — only a complex one — so this calculator restricts even degrees to non-negative numbers, while odd degrees (cube root, 5th root, …) accept negatives normally.
How exact-root detection works
Whenever the number you enter is a whole number, the calculator checks for a rigorous integer match — for example, confirming 3^3 = 27 exactly. For decimal inputs, it computes several extra guard digits beyond your requested precision and checks whether they settle into all zeros (or all nines), which signals the true decimal expansion terminates within that range. If neither holds, the root is irrational or simply doesn't terminate at the precision you asked for.
Privacy
This calculator runs entirely in your browser using exact arbitrary-precision integer arithmetic. Your numbers are never uploaded, logged, or stored.
Use it from code
From 3 credits per callREST API
curl -X POST https://api.iotools.cloud/v1/tool/nth-root-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"base": "27",
"degree": "3",
"precision": "20"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `nth-root-calculator` tool (Nth Root Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.