 
 
 
9.1.8  Multiplication by the conjugate quantity
The mult_conjugate
tries to remove square roots from the bottom of an expression.
- 
mult_conjugate takes
expr, an
expression. The denominator or numerator is supposed to contain a
square root.
- mult_conjugate(expr) returns the following:
- 
If expr is a fraction and the denominator contains a
square root, then this expression is returned with the numerator and
denominator multiplied by the conjugate of the denominator.
- If expr is a fraction and the numerator, but not the
denominator, contains a square root (if expr is not a
fraction, it is regarded as a fraction with a denominator of 1),
then this expression is returned with the numerator and denominator multiplied by the
conjugate of the numerator.
 
Examples
| mult_conjugate((2+sqrt(2))/(2+sqrt(3))) | 
|  | | |  | | | ⎛ ⎜
 ⎝
 | 2+ | √ |  | ⎞ ⎟
 ⎠
 | ⎛ ⎜
 ⎝
 | 2− | √ |  | ⎞ ⎟
 ⎠
 | 
 |  |  |  | | ⎛ ⎜
 ⎝
 | 2+ | √ |  | ⎞ ⎟
 ⎠
 | ⎛ ⎜
 ⎝
 | 2− | √ |  | ⎞ ⎟
 ⎠
 | 
 | 
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
| mult_conjugate((2+sqrt(2))/(sqrt(2)+sqrt(3))) | 
|  | | |  | | | ⎛ ⎜
 ⎝
 | 2+ | √ |  | ⎞ ⎟
 ⎠
 | ⎛ ⎜
 ⎝
 | − | √ |  | + | √ |  | ⎞ ⎟
 ⎠
 | 
 |  |  |  | | ⎛ ⎜
 ⎝
 | √ |  | + | √ |  | ⎞ ⎟
 ⎠
 | ⎛ ⎜
 ⎝
 | − | √ |  | + | √ |  | ⎞ ⎟
 ⎠
 | 
 | 
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
| mult_conjugate((2+sqrt(2))/2) | 
|  | | |  | | | ⎛ ⎜
 ⎝
 | 2+ | √ |  | ⎞ ⎟
 ⎠
 | ⎛ ⎜
 ⎝
 | 2− | √ |  | ⎞ ⎟
 ⎠
 | 
 |  |  |  |  | 
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
 
 
