What is "rationalisation"

n. (alternative spelling of rationalization English)

1. n. (psychiatry) a defense mechanism by which your true motivation is concealed by explaining your actions and feelings in a way that is not threatening [syn: rationalization]

2. the cognitive process of making something seem consistent with or based on reason [syn: rationalization]

3. (mathematics) the simplification of an expression or equation by eliminating radicals without changing the value of the expression or the roots of the equation [syn: rationalization]

4. the organization of a business according to scientific principles of management in order to increase efficiency [syn: rationalization]

5. systematic organization; the act of organizing something according to a system or a rationale [syn: systematization, systematisation, rationalization]

In elementary algebra, root rationalisation is a process by which radicals in the denominator of an algebraic fraction are eliminated.

If the denominator is a monomial in some radical, say $a{\sqrt[n]{x}}^k,$ with , rationalisation consists of multiplying the numerator and the denominator by $\sqrt[n]{x}^{n - k},$ and replacing ${\sqrt[n]{x}}^n$ by (if , the same replacement allows us to reduce until it becomes lower than .

If the denominator is linear in some square root, say $a+b\sqrt{x},$ rationalisation consists of multiplying the numerator and the denominator by $a-b\sqrt{x},$ and expanding the product in the denominator.

This technique may be extended to any algebraic denominator, by multiplying the numerator and the denominator by all algebraic conjugates of the denominator, and expanding the new denominator into the norm of the old denominator. However, except in special cases, the resulting fractions may have huge numerators and denominators, and, therefore, the technique is generally used only in the above elementary cases.