# Math 10 Week 2

This week I struggled with being positive. I wasn’t quite understanding how to convert mixed radicals to simplest form when it has an exponent of 3 or 4. I was getting very frustrated and thought I was going to fail the numbers test. I ended up going in after school and received help from a friend. I now understand it and i’m able to explain it to others.

Ex. $3\sqrt{162}$

Vocab:

Radical – The radical is the number under the line Ex. $\sqrt{162}$

Coefficient – The Coefficient is the Larger number on the outside Ex. $3\sqrt{162}$

Index – The index is the little number on the outside. Ex. $3\sqrt{162}$

How to convert the mixed radical into simplest form you need to:

1. Find all the prime factors from the radical, using a factor tree or a factor table.
2. Bring the coefficient over to the radical side. *** Any time that you are bringing in something from the outside in, the index should always come with it. There will be two now. One on the outside and one on the inside. (When it is attached to a number it is called an exponent).
3.  Break down the $3^4$ into its full form.
4. Circle any groups of 4 that you see.
5. One Group of four  = One of that number. Two groups = Two of the number.
6. Bring the two 3s outside.
7. Multiply the 3s together
8. You now have the simplest form of $3\sqrt{162}$

See below for pictures