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:
“If in the opinion of the Tsars authors were to be the servants of the state, in the opinion of the radical critics writers were to be the servants of the masses. The two lines of thought were bound to meet and join forces when at last, in our times, a new kind of regime the synthesis of a Hegelian triad, combined the idea of the masses with the idea of the state.”
—Vladimir Nabokov (1899–1977)
“The expressions of the poet cannot be analyzed; his sentence is one word, whose syllables are words. There are indeed no words quite worthy to be set to his music. But what matter if we do not hear the words always, if we hear the music?”
—Henry David Thoreau (1817–1862)