Root calculator
Enter the root degree and the number. The result appears at once; for a negative number and an even degree the calculator explains why there is no real root.
How to use this page
- Fill in the fields in the form above — the result recomputes at once, with no page reload.
- Under the result you will find the interpretation scale, if the calculator has one: it says which range your value fell into.
- The formula we use is shown lower on this page — you can check the arithmetic yourself.
- To compute the same for another game or variant, change it in the select field — prices and pools update automatically.
Further reading
Formula
ⁿ√x = x^(1/n) The nth root of a number x is the number which, raised to the power n, gives x. The square root of 16 is 4, because 4² = 16; the cube root of 27 is 3, because 3³ = 27. The calculator computes a root of any whole degree — also a high one, for example ⁷√128 = 2.
Only odd-degree roots of negative numbers exist: ³√(−8) = −2, because (−2)³ = −8. An even-degree root of a negative number is not a real number — no real number squared is negative. In that case the calculator shows a message instead of a result. We do not go into complex numbers, as everyday arithmetic does not need them.
The result is shown with six decimal places. When the root is a whole number (⁴√16 = 2) the calculator shows it exactly, without the rounding tail produced by raw floating-point arithmetic.
Frequently asked questions
What is the fourth root of 16?
2, because 2⁴ = 2 · 2 · 2 · 2 = 16.
Can you take the root of a negative number?
Only for an odd degree: ³√(−8) = −2, ⁵√(−32) = −2. An even-degree root of a negative number does not exist among real numbers.
How does a root differ from a fractional power?
It is the same calculation: ⁿ√x = x^(1/n). The power notation is handier in transformations, the root sign when reading the result.
See also
Arithmetic Mean
Enter numbers separated by commas and calculate the arithmetic mean online. The calculator will give you the s
Circle area and circumference calculator
Find circle area and circumference from radius or diameter. Choose a unit and see the formula with your values
Combinations, variations and permutations
Calculate the number of combinations, variations and permutations of n elements taken k at a time. Combinatori