MathBase

Nth Root Calculator

Square root, cube root, fourth root — all in one calculator.

Value

Root (n)

Result

ⁿ√x = x^(1/n)

What you entered

Value: 256Root (n): 4

1
4th root of 256
256^(1/4)= 4
2
Verification
4^4= 256

Result

Result: 4

The 4th root of 256 is 4.

Nth roots of common values

The nth root is the value raised to the power of one over n.

Value	n	Nth root
16	2	4.000000
27	3	3.000000
32	5	2.000000
100	4	3.162278
1000	3	10.000000
2	10	1.071773

The last row is the useful one in practice: the tenth root of 2 is 1.0718, meaning 7.18% growth compounded ten times doubles a quantity - which is the exact version of the Rule of 72 for a ten-year doubling. Nth roots are how you recover a compound growth rate from a total change, which is precisely what the CAGR calculator does. Note that 100 to the power one quarter gives 3.162278, the same as the square root of 10, because taking a fourth root is taking a square root twice.

Roots as fractional exponents

The nth root of x is simply x raised to the power 1/n — so ³√27 = 27^(1/3) = 3. This equivalence connects roots to the broader framework of exponents and makes them easy to compute with a calculator or programming language that supports fractional powers.

Where nth roots appear

Beyond basic algebra, nth roots appear in finance (CAGR uses an nth root over years), statistics (geometric mean), signal processing (RMS calculations), and physics (dimensional analysis). The cube root is especially common in volume-to-length conversions.

Frequently asked questions

I need to find the 5th root of 248832 — how do I calculate that?

Raise 248832 to the power 1/5: 248832^(0.2) = 12. This works because the nth root of x equals x^(1/n). Enter n = 5 and x = 248832 above and the calculator shows each step.

What's the difference between an nth root and a logarithm?

An nth root asks 'what number raised to n gives x?' — so ³√27 = 3. A logarithm asks 'what power of a base gives x?' — so log₃(27) = 3. They invert different operations: roots undo exponentiation by the exponent, logs undo it by the base. Try the logarithm calculator for base-focused problems.

When would I use a 4th or 5th root in real life?

The geometric mean of n values uses an nth root. In finance, CAGR over 5 years takes a 5th root. In statistics, the 4th root appears in certain normalization transforms. Any time you need to 'undo' raising something to a power, you reach for the corresponding root.