Nth root calculator
Enter a number and an integer root degree to calculate ⁿ√x, including real odd roots of negative numbers.
Nth root (ⁿ√x)
Find a real root using an integer degree.
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Result
Enter the values, then select Calculate.
How to use the nth root calculator
An nth root reverses a power: it finds y when yⁿ = x. This calculator handles real roots with integer degrees and preserves a simplified square-root form for supported positive integers.
Root calculation and simplified square roots
Nth-root mode finds the real number y for which yⁿ = x. The degree n must be a whole number from 2 through 1,000. Even-degree roots of negative numbers have no real result, while odd-degree roots do: the cube root of −125 is −5 because (−5)³ = −125.
For positive integer square roots up to 1,000,000, the result also shows a simplified radical when possible. For example, √72 becomes 6√2 because 72 = 36 × 2. A perfect square such as √144 is shown exactly as 12. Larger values and other degrees receive a numerical result only; this finite simplification limit keeps the calculator focused and predictable.
Square, cube, and higher-root examples
Enter 72 with degree 2 to see the exact form 6√2 and its decimal value. Enter 125 with degree 3 to get 5, or −125 with degree 3 to get −5.
For a higher root, 81 with degree 4 gives 3 because 3⁴ = 81. A negative number with an even degree is rejected because it has no real root.
Limits and exact forms
- The degree must be a whole number from 2 through 1,000.
- Negative radicands are accepted only with an odd degree.
- Simplified radicals are shown for positive integer square roots up to 1,000,000.
- Other supported roots show a numerical result, which may be approximate.
- Results use finite-precision browser arithmetic.
Frequently asked questions
Can I calculate an odd root of a negative number?
Yes. A negative radicand with an odd integer degree has a negative real root.
Why is a negative square root rejected?
An even power of a real number cannot be negative, so a negative radicand has no real even-degree root.
Why do I see both a radical and a decimal?
Supported square roots preserve an exact simplified form such as 6√2 and also provide a practical decimal value.
What root degrees are supported?
Enter any whole-number degree from 2 to 1,000.
How can I check an nth root?
Raise the result to the entered degree. It should return the original radicand within normal rounding precision.