nth Root Calculator

The nth root is a mathematical operation that involves finding the number which, when raised to the power of n, equals a given value. It is the inverse operation of exponentiation.
164=  2\sqrt[4]{16}=\;22
Photo of calculator author Wes NolteCreated by Wes Nolte.Last updated Apr 25, 2024.

The nth Root Calculator Formula

y=xny = \sqrt[n]{x}

Definition of the Nth Root Function

The nth root is denoted as √n or n^(1/n) and is typically represented with a radical symbol (√). The value of n specifies the degree of the root and determines the behavior of the operation.For example, if we take the square root (√) of a number, we are finding the value that, when squared, gives us the original number. The square root is the most common example of the nth root, with n = 2. The general form of the nth root operation is expressed as: √n(x)Here, "n" represents the degree of the root, and "x" is the value for which we are finding the nth root. The nth root operation essentially answers the question, "What number raised to the power of n equals x?" For example, if we take the cube root (∛) of 27, we are finding the value that, when cubed, equals 27. In this case, ∛27 = 3, because 3 raised to the power of 3 equals 27.The nth root can be applied to both positive and negative numbers, although the behavior differs based on whether n is even or odd. If n is even, taking the nth root of a negative number will result in a complex number. However, if n is odd, the nth root of a negative number will be a real number, typically with a negative sign.The nth root operation has various applications in mathematics, physics, engineering, and other fields. It is used in solving equations, calculating values, and understanding relationships between quantities.