# Documentation

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## Syntax

```radsimp(`z`)
```

## Description

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

`radsimp` and `simplifyRadical` are equivalent.

## Examples

### Example 1

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

```radsimp(3*sqrt(7)/(sqrt(7) - 2)), radsimp(sqrt(5 + 2*sqrt(6))); radsimp(sqrt(5*sqrt(3) + 6*sqrt(2))), radsimp(sqrt(3 + 2*sqrt(2)))```
``` ```
``` ```
`radsimp((1/2 + 1/4*3^(1/2))^(1/2))`
``` ```
`radsimp((5^(1/3) - 4^(1/3))^(1/2))`
``` ```
```radsimp(sqrt(3*sqrt(3 + 2*sqrt(5 - 12*sqrt(3 - 2*sqrt(2)))) + 14))```
``` ```
`radsimp(2*2^(1/4) + 2^(3/4) - (6*2^(1/2) + 8)^(1/2))`
``` ```
```radsimp(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 `radsimp`:

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

### Example 3

Use `radsimp` to simplify these arithmetical expressions containing variables:

`z := x/(sqrt(3) - 1) - x/2`
``` ```
`radsimp(z) = expand(radsimp(z))`
``` ```
`delete z:`

### Example 4

Use `radsimp` to simplify nested radicals. When simplifying nested radicals, `radsimp` tries to reduce the nesting depth:

```radsimp((6*2^(1/2) + 8)^(1/2)); radsimp(((32/5)^(1/5) - (27/5)^(1/5))^(1/3)); radsimp(sqrt((3+2^(1/3))^(1/2) * (4-2^(1/3))^(1/2)))```
``` ```
``` ```
``` ```

## Parameters

 `z`

## Return Values

Arithmetical expression.

## References

Borodin A., Fagin R., Hopcroft J.E., and Tompa M.: Decreasing the Nesting Depth of Expressions Involving Square Roots, JSC 1, 1985, pp. 169-188.

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