simplifying square roots

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Presentation Description

Shows how to simplify radicals by using perfect square factors of the radicand.

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Simplifying Square Roots : 

Simplifying Square Roots Using Perfect Square Factors

Review : 

Review Square and square root – inverse operations Ex. 1: √25 = 5, since 52 = 25 Ex. 2: √529 = 23, since 232 = 529

Terms Used with Radicals : 

Terms Used with Radicals The √ symbol is called the radical sign The root being taken (usually 2 – unwritten – for a square root) is the index The number inside the radical is the radicand √ 25 (2)

Perfect Square Factors : 

Perfect Square Factors Simplify perfect square factors of the radicand Ex. 1: √12 = √4∙3 = 2√3 Ex. 2: √32 = √16∙2 = 4√2 Ex. 3: 3√8 = 3√4∙2 = 3∙2√2 = 6√2

Practice Problem : 

Practice Problem Now try this Problem: Simplify √48 Solution: √48 = √16∙3 = 4√3 OR: √48 = √4∙12 = 2√12 = 2√4∙3 = 2∙2√3 = 4√3

Now Try These : 

Now Try These Hint: Look for factors of 4, 9, 25, or 49 1. Simplify √18 2. Simplify √27 3. Simplify 2√75 4. Simplify √98 (answers on the next slide)

Answers to previous problems : 

Answers to previous problems 1. √18 = 3√2 (click here to see the solution) 2. √27 = 3√3 (click here to see the solution) 3. 2√75 = 10√3 (click here to see the solution) 4. √98 = 7√2 (click here to see the solution)

The End : 

The End Did you miss any of the previous problems? If so, try them again. Then continue with the next content item of the lesson!

Solution for √18 : 

Solution for √18 √18 = √9 ∙2 = 3√2 Back

Solution for √27 : 

Solution for √27 √27 = √9 ∙3 = 3√3 Back

Solution for 2√75 : 

Solution for 2√75 2√75 = 2√25∙3 = 2∙5√3 = 10√3 Back

Solution for √98 : 

Solution for √98 √98 = √49 ∙2 = 7√2 Back