nth root (ⁿ√x)
Calculate the nth root of a number.
Graf funkce
Co je nth root
The nth root ⁿ√x is the inverse of the nth power. We have ⁿ√x = x^(1/n). For example ⁴√16 = 2, because 2⁴ = 16.
Where it is used in practice
- Average growth over a period (geometric mean) – e.g. average annual return of an investment.
- Scaling in multiple dimensions.
- Signal processing and acoustics.
Good to know
An even root (2nd, 4th, 6th…) of a negative number is not real. An odd root (3rd, 5th…) works for negative numbers too.
Rules of exponents
When working with powers it helps to know the basic rules, which always hold:
xⁿ · xᵖ = xⁿ⁺ᵖ (product – add the exponents)
xⁿ ÷ xᵖ = xⁿ⁻ᵖ (quotient – subtract the exponents)
(xⁿ)ᵖ = xⁿ·ᵖ (power of a power – multiply)
x⁻ⁿ = 1 / xⁿ (negative exponent)
x^(1/n) = ⁿ√x (root as a power)
In detail with examples: rules of exponents.
Tip: very large numbers are shown in shortened form – use scientific notation.