The document provides a tutorial on simplifying square roots using perfect square factors, explaining concepts such as the radical sign and radicand. It includes examples and practice problems, followed by solutions to reinforce learning. Key examples demonstrate how to simplify various square roots, emphasizing the identification of perfect square factors.

1. Simplifying Square Roots Using Perfect Square Factors

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

3. 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)

4. 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

5. 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

6. 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)

7. 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)

8. 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!

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

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

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

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