attempts to express all Root objects in expr in terms of radicals.

# Details and Options • ToRadicals can always give expressions in terms of radicals when the highest degree of the polynomial that appears in any Root object is four.
• There are some cases in which expressions involving radicals can in principle be given, but ToRadicals cannot find them.
• If Root objects in expr contain parameters, ToRadicals[expr] may yield a result that is not equal to expr for all values of the parameters.
• ToRadicals automatically threads over lists, as well as equations, inequalities, and logic functions.

# Examples

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## Scope(3)

All cubic Root objects can be converted into radicals:

All quartic Root objects can be converted into radicals:

Some higherdegree Root objects can be represented in terms of radicals:

ToRadicals also works with AlgebraicNumber objects:

## Generalizations & Extensions(1)

ToRadicals converts trigonometric functions of rational multiples of :

## Options(4)

### Cubics(2)

With the general formulas for solving cubic equations are not used:

Converting some cubic Root objects does not require the general formulas:

### Quartics(2)

With the general formulas for solving quartic equations are not used:

Converting some quartic Root objects does not require the general formulas:

## Properties & Relations(2)

RootReduce[ToRadicals[r]]==r for any algebraic number r given as a Root object:

By default Reduce will not produce radical solutions for general cubics:

Alternatively set :

## Possible Issues(3)

In this case ToRadicals succeeds on the unreduced expression:

In this case ToRadicals succeeds on the reduced expression:

ToRadicals converts Root objects containing parameters:

The result may not be equal to the Root object for some values of the parameter:

Introduced in 1996
(3.0)
|
Updated in 2003
(5.0)
2007
(6.0)