Simplified Form of A Radical Expression
A radical expression is said to be in simplified form if
- There is no factor of the radicand that can be written as a power greater than or equal to the index.
- There are no fractions under the radical sign.
- There are no radicals in the denominator.
For example, to write the radical expression in simplified form, we can proceed as follows. First, look for a perfect square under the square root sign and remove it:
Next, there is a fraction under the radical sign, which we change as follows:
Finally, we remove the radical from the denominator as follows:
When there is a denominator involving surds it may be possible to find a factor to multiply both numerator and denominator by to simplify the expression. For instance using the factorization of the sum of two cubes:
Simplifying radical expressions involving nested radicals can be quite difficult. It is not immediately obvious for instance that:
Read more about this topic: nth Root
Famous quotes containing the words simplified, form, radical and/or expression:
“I have simplified my politics into an utter detestation of all existing governments; and, as it is the shortest and most agreeable and summary feeling imaginable, the first moment of an universal republic would convert me into an advocate for single and uncontradicted despotism. The fact is, riches are power, and poverty is slavery all over the earth, and one sort of establishment is no better, nor worse, for a people than another.”
—George Gordon Noel Byron (1788–1824)
“Natural selection, the blind, unconscious, automatic process which Darwin discovered, and which we now know is the explanation for the existence and apparently purposeful form of all life, has no purpose in mind. It has no mind and no mind’s eye. It does not plan for the future. It has no vision, no foresight, no sight at all. If it can be said to play the role of the watchmaker in nature, it is the blind watchmaker.”
—Richard Dawkins (b. 1941)
“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)
“This is the great truth life has to teach us ... that gratification of our individual desires and expression of our personal preferences without consideration for their effect upon others brings in the end nothing but ruin and devastation.”
—Hortense Odlum (1892–?)