Radicals (also called roots) are the opposite of exponents. This is also called an inverse.

There are *actually* 3 parts to a radical. Square-roots don’t have an index because we assume it’s 2.

- the
**RADICAL** - the
**RADICAND** - the
**INDEX**

The **index** tells us how many identical factors we’re looking for.

We know the Radical & Radicand from simplifying square roots.

Example: since the index is 3, and there are 3- 5’s

### Procedure

Example:

To simplify radical expressions follow these steps.

**Step 1:** determine the index

The index is the small number in the angle of the radical symbol.

The index is 3.

**Step 2:** factor the radicand.

**Step 3:** pull out repeated factors of the amount of the index (in this case 3 times).

**Step 4:** repeated factors are removed from the radical and made single. All other factors stay inside the radical.

**Step 5:** Simplify