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Example:Rationalize the Denominator

 Post to:   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)