After our first unit test, I am feeling good about this semester in mathematics. We have moved on to radicals, and they are great! The piece I like the most about radicals is how the index changes how you look at the equation. It is integral to mixed and entire radicals.
The difference between a mixed and entire radical is whether there is a coefficient.
An entire radical would be something such as
![\sqrt[4]{32}](http://s0.wp.com/latex.php?latex=%5Csqrt%5B4%5D%7B32%7D&bg=ffffff&fg=000000&s=0 "\sqrt[4]{32}")
A mixed radical would be something such as
The cool thing is that you can convert each one to each other. Just watch.
For instance, take our previous example of a mixed radical
Since we have a group of numbers the same as the index (4 two’s), We can move those back inside the radical.
This means the same thing as
![\sqrt[4]{2 \bullet 2 \bullet 2 \bullet 2 \bullet 2}](http://s0.wp.com/latex.php?latex=%5Csqrt%5B4%5D%7B2+%5Cbullet+2+%5Cbullet+2+%5Cbullet+2+%5Cbullet+2%7D&bg=ffffff&fg=000000&s=0 "\sqrt[4]{2 \bullet 2 \bullet 2 \bullet 2 \bullet 2}")
In other words, it’s the fourth root of
Now we can easily figure out that ![2\sqrt[4]{2}](http://s0.wp.com/latex.php?latex=2%5Csqrt%5B4%5D%7B2%7D&bg=ffffff&fg=000000&s=0 "2\sqrt[4]{2}")
How cool is that!