# Documentation

### This is machine translation

Translated by
Mouse over text to see original. Click the button below to return to the English verison of the page.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

## Description

simplifyRadical(z) tries to simplify the radicals in the expression z. The result is mathematically equivalent to z.

## Examples

### Example 1

Simplify these constant expressions with square roots and higher order radicals:

simplifyRadical(sqrt(3*sqrt(3 + 2*sqrt(5 - 12*sqrt(3 - 2*sqrt(2))))
+ 14))

simplifyRadical(2*2^(1/4) + 2^(3/4) - (6*2^(1/2) + 8)^(1/2))

simplifyRadical(sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3))
- sqrt(10 + 6*sqrt(3)))

### Example 2

Create the following expression and then simplify it using simplifyRadical:

x := sqrt(3)*I/2 + 1/2: y := x^(1/3) + x^(-1/3): z := y^3 - 3*y

delete x, y, z:

### Example 3

Use simplifyRadical to simplify these arithmetical expressions containing variables:

z := x/(sqrt(3) - 1) - x/2

delete z:

 z

## Return Values

Arithmetical expression.

## Algorithms

For constant algebraic expressions, simplifyRadical constructs a tower of algebraic extensions of using the domain Dom::AlgebraicExtension. It tries to return the simplest possible form.

This function is based on an algorithm described in Borodin, Fagin, Hopcroft and Tompa, "Decreasing the Nesting Depth of Expressions Involving Square Roots", JSC 1, 1985, pp. 169-188.In some special cases, an algorithm based on Landau, "How to tangle with a nested radical", The Mathematical Intelligencer 16, 1994, no. 2, pp. 49-55, is used.