What an nth root means
The nth root of a number is the value that, raised to the power n, gives you back the original number. Taking a root is the inverse of raising to a power, so the square root of 9 is 3 because 3 squared is 9, and the cube root of 27 is 3 because 3 cubed is 27.
Mathematically this is the same as raising the number to the fractional power 1/n. That is how the calculator computes it, which means the degree does not have to be a whole number; you can take any real-valued root.
Reading the result
Most roots are irrational, so the answer is shown as a decimal approximation rather than an exact figure. The square root of 2, for example, displays as roughly 1.41421, never as a number that terminates.
- Degree 2 gives the square root
- Degree 3 gives the cube root
- Higher degrees produce values closer to 1 for inputs above 1
- A fractional degree such as 0.5 is also valid and inverts a power
Negative numbers and signs
Odd roots of negative numbers are real and keep the negative sign: the cube root of -8 is -2. Even roots of negative numbers, however, have no real value, because no real number squared (or raised to any even power) can be negative.
For that reason the calculator accepts the cube root of a negative input but rejects the square root of one, returning an error rather than an imaginary result.
Common mistakes
The most frequent errors come from confusing the root with the power, or from expecting an exact answer to an inherently irrational one. A degree of zero is undefined and is rejected, since the operation has no meaning.
- Do not confuse degree (the n) with the value being rooted
- Expect rounded decimals for most non-perfect roots
- Use an odd degree for negative inputs to get a real answer
- A degree of zero is not allowed
Formula
result = value^(1/degree)