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radsimp -- simplify radicals in arithmetical expressions

Introduction

radsimp simplifies arithmetical expressions containing radicals.

Call(s)

radsimp(z)

Parameters

z - an arithmetical expression

Returns

an arithmetical expression.

Further Documentation

Chapter ``Manipulating Expressions'' of the Tutorial.

Related Functions

combine, ifactor, normal, rectform, simplify

Details

Example 1

We demonstrate the simplification of constant expressions with square roots and higher order radicals:

>> radsimp(2*2^(1/4) + 2^(3/4) - (6*2^(1/2) + 8)^(1/2))
                                     0
>> radsimp(
     sqrt(14 + 3*sqrt(3 + 2*sqrt(5 - 12*sqrt(3 - 2*sqrt(2)))))
   )
                                  1/2
                                 2    + 3
>> radsimp(3*sqrt(7)/(sqrt(7) - 2))
                                   1/2
                                2 7    + 7
>> radsimp(sqrt(1 + sqrt(3)) + sqrt(3 + 3*sqrt(3)) 
                - sqrt(10 + 6*sqrt(3)))
                                     0
>> x := sqrt(3)*I/2 + 1/2: y := x^(1/3) + x^(-1/3): z := y^3 - 3*y
      /           1                     1/2       1/3 \3
      | --------------------- + (1/2 I 3    + 1/2)    |  -
      |         1/2       1/3                         |
      \ (1/2 I 3    + 1/2)                            /
      
                   1/2       1/3             3
         3 (1/2 I 3    + 1/2)    - ---------------------
                                           1/2       1/3
                                   (1/2 I 3    + 1/2)
>> radsimp(z)
                                     1
>> delete x, y, z:

Example 2

radsimp also works on arithmetical expressions containing variables:

>> z := x/(sqrt(3) - 1) - x/2
                                  x       x
                               -------- - -
                                1/2       2
                               3    - 1
>> radsimp(z) = expand(radsimp(z))
                         /  1/2       \          1/2
                         | 3          |   x   x 3
                       x | ---- + 1/2 | - - = ------
                         \  2         /   2     2
>> delete z:

Background

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