nth Root - Simplified Form of A Radical Expression

Simplified Form of A Radical Expression

A radical expression is said to be in simplified form if

  1. There is no factor of the radicand that can be written as a power greater than or equal to the index.
  2. There are no fractions under the radical sign.
  3. 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)

    “Every neurosis is a primitive form of legal proceeding in which the accused carries on the prosecution, imposes judgment and executes the sentence: all to the end that someone else should not perform the same process.”
    —Lionel Trilling (1905–1975)

    “A radical is one of whom people say “He goes too far.” A conservative, on the other hand, is one who “doesn’t go far enough.” Then there is the reactionary, “one who doesn’t go at all.” All these terms are more or less objectionable, wherefore we have coined the term “progressive.” I should say that a progressive is one who insists upon recognizing new facts as they present themselves—one who adjusts legislation to these new facts.”
    —Woodrow Wilson (1856–1924)

    “Here and there a bird sang, a rose silenced her expression of him, and all the gaga flowers wondered. But they puzzled the wanderer with their vague wearinesses.”
    —John Ashbery (b. 1927)