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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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Why do you need to rationalize the denominator?
It is basically a convention for a standardized form.
You can only use conjugates to rationalize the denominator when the denominator contains one radical term?
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.
What is the rationalizes denominator of 42 divided by the square root of 7?
6
Rationalize 5 over square root of 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.
Can two irrational numbers have a product as rational?
Yes. A simple example: sqrt(2)*sqrt(2) = 2 This property is used to "simplify" (rationalise the denominator of) surds.
