Simplifying Radicals.

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Presentation transcript:

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. Example: 200 = 100∙2 = 100 ∙ 2 Take the square root of the P.S. radical and “free” it. Leaving the second radical alone. Example: 200 = 100∙2 = 100 ∙ 2 =10∙ 2

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

Getting Rid of a Radical in the Denominator

First things first… How do you undo square root? What do you get when you square the square root of 6? 6 2 = Trick question…What is 6 6 ? We call this a “crafty” form of 1.

We don’t like having radicals in our denominators! To get rid of a radical in the denominator you must: Multiply the entire fraction by a “crafty” form of 1. (remember when multiplying fractions multiply across the top, multiply across the bottom) Example: 4 2 ∙ 2 2 = 4∙ 2 2 ∙ 2 Simplify the denominator. Example: 4 2 ∙ 2 2 = 4∙ 2 2 ∙ 2 = 4∙ 2 2 Simplify the numerator and denominator if possible. Example: 4 2 ∙ 2 2 = 4∙ 2 2 ∙ 2 = 4∙ 2 2 = 2∙ 2 1 =2 2

Practice Simplify the following fractions: 5 3 10 2 3 6 11 5 8 3