Radical 

A radical is an expression in the form ofAn example of a radical is It includes a index, radicand, and radical symbol, making all together a radical. In this case the index is 5 and the radicand is 125. 

Note:

If the index is not written, as in square root, it is assumed to be 2.

The index is the number of times the radical must be multiplied by itself to equal the radicand.

An entire radical is when the number is entirely under the root symbol or the radical sign. Whereas a mixed radical isn’t. A mixed radical is a form of simplifying an entire radical.

 

 

 

Converting an entire radical to a mixed radical

To convert or simplify an entire radical, you need to find two factors of the number, one being a perfect root. For example,

4 being the perfect root in this case. Then each of those factors become a radical, leaving you with radical that isn’t a whole number (because it is not perfect, and becomes a decimal if rooted). You are then left with a mixed radical. 

If you wish to simplify it futher, you need to repeat the process by finding another perfect root that is a factor of the radicand. 

Converting a mixed radical back to an entire radical

You need to put the number on the outside of the radical sing back under the sign. To do this, you use the index as an exponent for that number. Than multiply it by the radicand. You end up with an entire radical.

 

This week we learned about Radicals, mixed radicals to entire radicals, and entire radicals to mixed, no matter what the index is. One challenge with this lesson is remembering all the steps. In order to make sure that your end result is correct, you need to make sure you don’t forget any step and write everything down so you do not get confused. If you forget to write out each factor as a radical, you can forget to find the roots, therefore leaving you confused. Once I got the hang of it, it became a very easy lesson/subject.