Simplify Radicals There are three rules that
must be observed in order to 1) all perfect powers of the radicand must be simplified according to the
2) the radicand must have no fractions,
this can be easily circumvented using the 3) no denominator can contain a radical. The third checkpoint could
pose a problem. (1) The For example, it is true that _{} and that _{} is a perfect square factor of _{}.However upon observation of _{}, we find that _{}. So _{} is not the “largest” perfect square factor of _{}. In fact _{} and _{} are both perfect square factors of 72 and therefore
_{} is the largest perfect square factor of _{}. To this radical, you
must factor the largest perfect square factor; therefore, fully simplify_{}. To simplify a radical containing variable/s, factor
the greatest perfect power of the index which would be the greatest
multiple of the index and then divide the exponent of the largest perfect
factor by the index and remove the radical. For example, _{}, but _{}. When radicals containing variables are fully
simplified, there will be no variable under the radical which will have an
exponent greater than or equal to the index. For example, while it is
true that _{}there are variables with exponents higher than the index
still left under the radical. To fully simplify, _{}.(2) The (3) For example, if we were to simplify the following problem with the following result, then the radical expression would not be "fully simplified" because there is a radical left in the denominator. Example 1: To "rationalize" the denominator multiply the denominator by so that to maintain the equality of the fraction. So now we would have ... Now the fraction is "fully simplified"
Example 2:
... Notice that the numerator is also a radical, so multiply Example 3:
... Simplify the numerator and denominator The views and
opinions expressed in this page are strictly those of Mary Lou Baker. This page was edited on 15-Nov-2007 |