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Example:Rationalize the Denominator

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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


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).





The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.