Radical Expressions
A fraction may also contain radicals in the numerator and/or the denominator. If the denominator contains radicals, it can be helpful to rationalize it (compare Simplified form of a radical expression), especially if further operations, such as adding or comparing that fraction to another, are to be carried out. It is also more convenient if division is to be done manually. When the denominator is a monomial square root, it can be rationalized by multiplying both the top and the bottom of the fraction by the denominator:
The process of rationalization of binomial denominators involves multiplying the top and the bottom of a fraction by the conjugate of the denominator so that the denominator becomes a rational number. For example:
Even if this process results in the numerator being irrational, like in the examples above, the process may still facilitate subsequent manipulations by reducing the number of irrationals one has to work with in the denominator.
Read more about this topic: Numerator (fraction)
Famous quotes containing the words radical and/or expressions:
“To the indefinite, uncertain mind of the American radical the most contradictory ideas and methods are possible. The result is a sad chaos in the radical movement, a sort of intellectual hash, which has neither taste nor character.”
—Emma Goldman (1869–1940)
“Each child has his own individual expressions to offer to the world. That expression can take many forms, from artistic interests, a way of thinking, athletic activities, a particular style of dressing, musical talents, different hobbies, etc. Our job is to join our children in discovering who they are.”
—Stephanie Martson (20th century)