How do we rationalize the denominations of radicals?

Answer 1

The complex conjugate of a denominator is similar to the original denominator, except with a different operation. For my example, sq(x) is the square root of x.

Ex: if the denominator that you are trying to rationalize is 5+sq(8), then the complex conjugate would be 5 - sq(8).

So you would take your original fraction, lets say:
4
------------
5 + sq(8)
and you would multiply it by the complex
conjugate over itself, basically multiplying
by 1. It would look like this (don't mind the periods, they are simply there to space the fractions correctly):

..... 4 ..............5 - sq(8) ....... 20 - 4sq(8)
---------------- x ---------------- = ------------------------
. 5 + sq(8) ...... 5 - sq(8) .... 25+5sq(8)-5sq(8) - 8


Finally, the denominator in your answer would simplify out leaving you with a final RATIONALIZED fraction of:

20 - 4sq(8)
------------------------
17

Hope this helps

Answer 2

by multiplying suitably the denominator to remove the radical sign and the numerator in order that the value is not changed
follow these rules if you have (n)^1/2 multiply by (n)^1/2.if it is (n)^1/3 multiply by (n)^2/3 if the numerator is a monomial.if it is a binomial multiply by the conjugate
e.g. if you have (a)^1/2-(b)^1/2 multipl7y by (a)^1/2+(b)^1/2 and if you have (a)^1/2-(b)^1/2 multiply by (a)^1/2+(b)^1/2

Answer 3

by multiplying the radical by itself or by multiplying by its conjugate.

Answer 4

You use conjugates