Simplifying Radicals

A radical is any algebraic statement with this symbol: What is a Radical? A radical is any algebraic statement with this symbol: 2 This is called the RADICAL The number under here is called the RADICAND

Before you can simplify… We need to know what a perfect square is! A perfect square is any number created by squaring another number. Ex: 3 2 =9 9 is the perfect square! Ex: 10 2 =100 100 is the perfect square!

What are all the perfect squares up to 100? 1 2 =1 2 2 =4 3 2 =9 4 2 =16 5 2 =25 6 2 =36 7 2 =49 8 2 =64 9 2 =81 10 2 =100 These are the perfect squares

First 10 Perfect Squares It would be a good idea to write down and memorize the first 10 perfect squares! Here they are again: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Now that we know our P.S.’s we can begin Find the biggest Perfect Square that goes into the RADICAND (the number under the radical) evenly. Example: 200 = 100∙2 (always put the P.S. first) Separate the radical into two new radicals. Take the square root of the P.S. radical and “free” it. Leaving the second radical alone.

Practice Simplify the following radicals if possible. 75 32 27 13 8

Some like you’ve seen before… 16± 32 4 9± 72 3 24± 28 8

What if the radical is being multiplied by something else? Follow the same steps for simplifying the radical part. Once you have the simplified radical, multiply the two “freed” numbers, and leave the simplified radical as is. Example: Simplify: 7 600