nth Roots and the Index

The little number that tells you what root to take is called the INDEX.
If there is no index written, THE INDEX IS 2 (a square root).

You need to become familiar with these perfect powers!
You should be able to use all powers to the 1st, 2nd, 3rd, & 4th powers. And the 5th powers of 2, 3, & 4.

You will get one on paper in class.

​​Perfect Powers Chart

You need to know what these words mean when you hear me use them!

Vocabulary

To simplify a square root, look for a factor of the number that is a perfect square & simplify what you can.

Ideally, you want to find the biggest perfect square factor.

Review: Simplify Square Roots

Not the Biggest?

To simplify a higher root, you use a similar strategy!

If you have a 3rd root, you need to find a perfect cube that is a factor. 4th root, find a perfect fourth, and so on…

Simplifying Higher Roots

Pause for examples on whiteboard...

​With variables, the process it the same, but the perfects look different.

Perfect roots in variables are any power that is a multiple of the index.

Simplifying Variable Roots

​What you are doing is pulling out groups of the variable the value of the index.

You probably will not have to go through this process each time, but this is good to have in your notes to visualize.

When you cannot simplify a term any more, CIRCLE IT!

​Remember: YOU ONLY TAKE THE SQUARE ROOT ONE TIME!

Pause for examples on whiteboard...