Explanation:
Rationalisation (mathematics)
In elementary
algebra root rationalisation is a process by which surds in the denominator of a fraction are eliminated.
These surds may be monomials or binomials involving square roots, in simple examples.
There are wide extensions to the technique.
Rationalization
of a monomial square root and cube root
For the fundamental technique, the numerator and denominator must
be multiplied, but by the same factor.
Example 1:
To rationalize this kind of monomial, bring in the factor:
The square root disappears from the denominator, because it is squared:
This gives the result, after simplification:
�(Our solved example in
mathguru.com uses this concept).
Dealing
with more square roots
For a denominator that is:
Rationalisation can be achieved by multiplying by the Conjugate:
and applying the difference of two squares identity, which here will yield −1. To get this result, the
entire fraction should be multiplied by
This technique works much more generally. It can easily be adapted
to remove one square root at a time, i.e. To Rationalise
by multiplication by
Example:
The fraction must be multiplied by a quotient containing.
Now, we can proceed to remove the square roots in the
denominator:
(Our solved example in mathguru.com uses this concept).
http://en.wikipedia.org/wiki/Rationalisation_(mathematics)
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