nth Root & Cube Root Calculator NZ

This calculator finds the nth root of any number, the value that, raised to the power n, gives your number back. It covers the cube root, the fourth root, the fifth root and beyond, as well as showing the square root and cube root alongside for quick reference. Roots are the inverse of powers: just as the square root undoes squaring, the cube root undoes cubing, and the nth root undoes raising to the nth power. They appear constantly in geometry, where the cube root recovers a side length from a volume, in finance, where roots are used to find average growth rates, in science and in everyday problem solving. Calculating anything beyond a square root by hand is awkward, which is where this tool helps. You enter the number and the root you want, n, and the calculator returns the nth root, along with the cube root and square root of the same number for convenience. The results update as you type, so you can explore how different roots of a number compare. Use it for maths homework, to recover a dimension from a volume or area, to work out a compound growth rate, or whenever you need a root quickly and accurately. A note on negatives: even roots, such as the square or fourth root, of a negative number are not real, so the calculator handles odd roots of negatives, like the cube root of minus 8 being minus 2, but flags even roots of negatives as undefined in the real numbers. The calculation is precise, rounded for display.

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4
nth root of the number
Cube root4
Square root8
Check4^3 ≈ 64

The nth root undoes raising to the power n. Even roots of negative numbers are not real and are flagged. Rounded for display.

How it works

The nth root of a number is that number raised to the power one over n. The calculator computes this directly, handling odd roots of negative numbers by taking the root of the absolute value and restoring the negative sign. Even roots of negative numbers are undefined in the real numbers and are flagged.

Worked example

The cube root of 64 is the number that cubed gives 64, which is 4, because 4 times 4 times 4 is 64. The square root of 64 is 8. The fifth root of 64 is about 2.297. For a negative example, the cube root of minus 8 is minus 2, but the square root of minus 8 is undefined in the real numbers.

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Frequently asked questions

How do I calculate the nth root?

The nth root of a number is that number raised to the power of one divided by n. For example, the cube root is the power one third, and the fourth root is the power one quarter. This calculator computes any nth root, plus the square and cube roots.

Can you take the root of a negative number?

Odd roots of negative numbers are fine: the cube root of minus 8 is minus 2. But even roots, such as the square or fourth root of a negative number, are not real numbers, because no real number squared gives a negative. The calculator flags these cases.

What is the cube root used for?

The cube root recovers a length from a volume, since volume is a length cubed. It also appears in scaling problems and some growth-rate calculations. This calculator shows the cube root alongside any nth root you choose.