Nth root calculator with square, cube and real roots
Enter a radicand and whole-number index. HitEquals returns the principal real nth root, reciprocal exponent, verification power and nearby integer powers.
Inputs used by this calculator
Root Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Radicand (x) | 256 | Any finite number supported by the formula | Supplies the radicand (x) quantity used by the published equation or result breakdown. |
| Root index (n) | 4 | 1 to 1000 | Supplies the root index (n) quantity used by the published equation or result breakdown. |
What an nth root means
The nth root of x is a value y satisfying yⁿ=x. The radical index is n.
Roots as rational exponents
A root can be written using the reciprocal exponent 1/n.
ⁿ√x=x^(1/n)Square and cube roots
Square root uses index two; cube root uses index three. The displayed result is the principal real root.
Negative radicands
Odd powers preserve sign and therefore negative numbers have negative odd roots. Even powers cannot produce a negative real value.
Worked fourth-root example
Because 4×4×4×4=256, the fourth root of 256 is 4.
Numerical scope
Floating-point verification may differ in its last displayed digits for irrational roots. The page does not simplify symbolic radicals or find roots of polynomials.
Common root notation
| Name | Radical | Exponent |
|---|---|---|
| Square root | √x | x^(1/2) |
| Cube root | ∛x | x^(1/3) |
| Fourth root | ⁴√x | x^(1/4) |
| nth root | ⁿ√x | x^(1/n) |
Frequently asked questions
What is the fourth root of 256?
It is 4.
Can a negative number have a square root?
Not in the real numbers.
Can a negative number have a cube root?
Yes.
Is nth root the same as power 1/n?
Yes in the supported real domain.
Why is the square root called principal?
The radical symbol denotes the nonnegative root even though y²=x may have two solutions.
Does this solve polynomial equations?
No.
What to keep in mind
This calculator returns the principal real nth root. An even-degree root of a negative number requires complex numbers and is outside scope. Polynomial roots are a different problem.
Results are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.