Nth Root

An nth root of a real (or complex) number $ a $, denoted $ \sqrt[N]{a} $, is a number $ x $ such that $ x^N = a $, where $ N $ is a non-zero natural number ($ N \geq 2 $)

Note: for a negative real number $ a $ and $ N $ is even, the nth root does not exist in the set of real numbers.

Calculating the nth root of a number $ a $ is equivalent to calculating $ a^{1/N} $ and taking only the principal real root.

To calculate complex roots, solve the equation $ x^N = a $ in $ \mathbb{C} $, that is equivalent to searching the complex roots of the polynomial of degree $ N $: $ x^N - a = 0 $

Most scientific calculators allow you to calculate an Nth root using a dedicated key or function (symbol ⁿ√).

Alternatively, enter the calculation $ a^{1/N} $ using the x^y or ^ key.

With spreadsheets like Microsoft Excel, use the power formula: for a value in A1 and a value N in A2, write =A1^(1/A2) or =POWER(A1;1/A2)

The root simplifyer will attempt to extract the obvious factors:

Simplification can be done manually in steps:

— Decompose the number into prime factors

— Identify the factors that are repeated N times

— Remove this factor from the radical

The term surd refers to a mathematical expression containing a root that cannot be simplified into a rational number.

The Unicode standard offers the group of two symbols √, namely U+207F ⁿ and U+221A √

In LaTeX, write \sqrt[N]{x}

In programming languages, write x**(1/N)