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:
“Our conscience is not the vessel of eternal verities. It grows with our social life, and a new social condition means a radical change in conscience.”
—Walter Lippmann (1889–1974)
“Many expressions in the New Testament come naturally to the lips of all Protestants, and it furnishes the most pregnant and practical texts. There is no harmless dreaming, no wise speculation in it, but everywhere a substratum of good sense. It never reflects, but it repents. There is no poetry in it, we may say, nothing regarded in the light of beauty merely, but moral truth is its object. All mortals are convicted by its conscience.”
—Henry David Thoreau (1817–1862)