Fourth Root
Calculate the fourth root (^4sqrtx) of any real number instantly using sqrt(sqrtx). Free online fourth root calculator supports positive and negative values with precise results.
About This Calculator
The Fourth Root Calculator computes the fourth root (^4sqrtx) of any non-negative real number. The fourth root of a number x is the value that when multiplied by itself four times equals x. Mathematically, ^4sqrtx = x^(1/4) = sqrt(sqrtx). This calculator uses Math.sqrt(Math.sqrt(x)) for efficient computation.
Since the fourth root involves an even exponent (4), it is only defined for non-negative real numbers when working in the real number system. For positive inputs, both the positive and negative fourth roots exist (e.g., ^4sqrt16 = +/-2), but this calculator returns the principal (positive) fourth root. For negative inputs, the fourth root is not a real number.
Fourth roots appear in engineering applications (beam deflection, moment of inertia where radius appears to the fourth power), in statistics (kurtosis and fourth central moments), and in geometry (calculating dimensions from hypervolumes). This tool is ideal for students and professionals who need quick and precise fourth root calculations.
Frequently Asked Questions
What is a fourth root?
The fourth root of a number x is a number that when multiplied by itself four times gives x. It is written as ^4sqrtx or x^(1/4). For example, ^4sqrt16 = 2 because 2 x 2 x 2 x 2 = 2^4 = 16.
Can you find the fourth root of a negative number?
The fourth root of a negative number is not a real number because any real number raised to the 4th power (an even power) gives a non-negative result.
How is the fourth root calculated?
The fourth root can be calculated as the square root of the square root: ^4sqrtx = sqrt(sqrtx). For example, ^4sqrt81 = sqrt(sqrt81) = sqrt9 = 3.
Where is the fourth root used in real life?
Fourth roots appear in engineering (moment of inertia, beam deflection), physics (wave mechanics), statistics (kurtosis), and finance (geometric mean over 4 periods).
What is the relationship between square root and fourth root?
The fourth root is the square root of the square root: ^4sqrtx = sqrt(sqrtx). The fourth root grows faster than higher roots but slower than square roots.