**Some Necessary Vocabulary**The radicand refers to the number under the radical sign. In the radical below, the radicand is the number '5'.

**Video** in How To Simplify Radicals

### Some Necessary Background Knowledg

#### I. Know your Perfect Squares!

Before you learn how to simplify radicals,you need to be familiar with what a perfect square is. Also, you should be able to create a list of the first several perfect squares. This is easy to do by just multiplying numbers by themselves as shown in the table below.

List Perfect Squares | |
---|---|

2*2 | 4 |

3*3 | 9 |

4*4 | 16 |

5*5 | 25 |

6*6 | 36 |

7*7 | 49 |

8*8 | 64 |

9*9 | 81 |

10*10 | 100 |

11*11 | 121 |

12*12 | 144 |

13*13 | 169 |

#### II. You can rewrite a radical as the product of two radical factors of its radicand !

That's a very fancy way of saying that you can rewrite radicals as shown in the table below

Original Radical | Radical rewritten as product of factors |
---|---|

### How to Simplify Radicals Steps

Let's look at to help us understand the steps involving in simplifying radicals.

Step 1Find the largest perfect square that is a factor of the radicand

4 is the largest perfect square that is a factor of 8

Rewrite the radical as a product of the square root of 4 (found in last step) and its matching factor(2)

Simplify