An example may help. If you have the fraction 1 / (2 + root(3)), where root() is the square root function, you multiply top and bottom by (2 - root(3)). If you multiply everything out, you will have no square root in the denominator, instead, you will have a square root in the numerator.
If the denominator is only a root, eg root(3), you multiply top and bottom by root(3).
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It is basically a convention for a standardized form.
No, you can also use conjugates with more than one radical term. For example, if the denominator is root(2) + root(3), you can use the conjugate root(2) - root(3) to rationalize the denominator.
6
The idea is to get rid of the square root in the denominator. For this purpose, you must multiply numerator and denominator by the square root of 6 in this case.
Yes. A simple example: sqrt(2)*sqrt(2) = 2 This property is used to "simplify" (rationalise the denominator of) surds.