Fifth Root
Calculate the fifth root (^5sqrtx) of any real number using x^(1/5). Free online fifth root calculator supports positive and negative values with high precision results.
About This Calculator
The Fifth Root Calculator computes the fifth root (^5sqrtx) of any real number. The fifth root of a number x is the value that when multiplied by itself five times equals x. Mathematically, ^5sqrtx = x^(1/5). This is the inverse operation of raising a number to the 5th power (x^5).
Unlike even roots (square root, fourth root) which are only real for non-negative numbers, the fifth root (being an odd root) is defined for all real numbers including negatives. For example, ^5sqrt32 = 2, ^5sqrt1 = 1, ^5sqrt0 = 0, and ^5sqrt(-32) = -2. The calculator uses JavaScript's Math.pow() function with the exponent 1/5 for precise computation.
Fifth roots are used in physics for certain decay and wave equations, in engineering for scaling calculations, and in mathematics for understanding inverse power relationships. This tool is ideal for students learning about radicals, engineers performing root calculations, and anyone who needs quick fifth root values.
Frequently Asked Questions
What is a fifth root?
The fifth root of a number x is a number that when multiplied by itself five times gives x. It is written as ^5sqrtx or x^(1/5). For example, ^5sqrt32 = 2 because 2 x 2 x 2 x 2 x 2 = 2^5 = 32.
Can you find the fifth root of a negative number?
Yes, the fifth root of a negative number is defined and real because an odd root of a negative number is negative. For example, ^5sqrt(-32) = -2 because (-2)^5 = -32.
How is the fifth root calculated?
The fifth root is calculated by raising the number to the power of 1/5: ^5sqrtx = x^(1/5). For example, ^5sqrt100 = 100^(1/5) ≈ 2.5119.
Where is the fifth root used in real life?
Fifth roots appear in physics (inverse square law variations), engineering (material stress calculations), finance (geometric mean over 5 periods), and computer science (algorithm analysis).
What is the difference between square root and fifth root?
The square root asks what number multiplied by itself twice gives x. The fifth root asks what number multiplied by itself five times gives x. Fifth roots grow more slowly than square roots.