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 (17881824)
“The Republican form of government is the highest form of government; but because of this it requires the highest type of human naturea type nowhere at present existing.”
—Herbert Spencer (18201903)
“Universal suffrage is sound in principle. The radical element is right.”
—Rutherford Birchard Hayes (18221893)
“... if the Settlement seeks its expression through social activity, it must learn the difference between mere social unrest and spiritual impulse.”
—Jane Addams (18601935)