Math Blog Week 2

In math this week we learned about radicals, mixed radicals, and entire radicals.

A radical is the term used for any root number like 

A mixed radical is when a radical is expressed as a root with a coefficient like 

Entire radicals are radicals that have no numbers in front of them like .

Entire radicals can be converted into mixed radicals and vice versa. To convert a radical into a mixed one first take let’s say , to convert this to a mixed fraction first remember the values of perfect squares like 4, 9, 16, or 25, always start with the smallest perfect square and see if the root is divisible by that one for example for the lowest square it’s divisible by is , 20 divided by 4 is 5 so  is , because 4 is a perfect square we can turn it into its square root which is 2, is not a perfect square and has no factors that are so it is in its simplest form, meaning that the simplest mixed radical form of  is .

If everything goes right your equation or thought process should look something like this:

=

= 2

The opposite is even easier in my opinion, to convert a mixed radical into an entire one first take a number for example , all you have to do to find the answer is first square the coefficient which is the 7,  is 49 so our answer would be  which is  (the multiplication there isn’t actually that simple you may want a calculator).

=

=

If the radical is a cube root, fourth root or higher you’ll need to calculate a bit differently mixed into entire you’ll need to multiply the coefficient by itself more than once and for entire into mixed you’ll need to find perfect cubes or other for dividing the radical.