Simplifying Radical Expressions

1. Simplifying Radical Expressions Essential Question: How do you use square roots to simplify radical expressions? SPI: 706.2.3:Use rational numbers and roots of perfect squares/cubes to solve contextual problems

2. Activator Simplify the square root of 72 using factorization: √72

3. Simplifying Radical Expressions • The following are examples of radical expressions: √16*√9, √(4+25), √36/9, √xy

4. Essential Question: How do you use square roots to simplify radical expressions? Simplifying Radical Expressions

5. Simplifying multiplication under a radical: You can multiply the radicals first and then simplify or you can simplify each radical then multiply: Ex: √8*4 = √2*2*2*2*2 = 4√2 or √4*16 = √4 * √16 = 2*4=8

6. Simplifying Multiplication Expressions √25*81 (Partners, tell each other what you would do first.) Solve: √25*81

7. When the Numbers Are Not Perfect Squares

8. On Your Own √9 * √4 √27(3) √6 * √6 √x2 After the last two problems, what rule can you come up with to explain what happens when you square root a squared number?

9. In Your Own Words • Explain the best way to simplify radical expressions involving multiplication.

10. Simplifying division under a radical: First you must determine what is under the radical: Ex: √49/25, √16 / 2, 24/√64 If the whole problem is under the radical, you simplify or divide first. If only one part is under the radical, you must simplify that part first. Simplifying multiplication under a radical: You can multiply the radicals first and then simplify or you can simplify each radical then multiply: Ex: √8*4 = 4√2 or √4*16 = √4 * √16 = 2*4=8

11. Simplifying Division Expressions √64 25 (Both #s are under the same radical) Tell your neighbor what you would do first. When both numbers are under the same radical you can simplify each # first or you can divide then find the square root. Solve: √100 16

12. On Your Own √128 (both #s are under the radical) 8 √25 (only 25 is under the radical) 5 100 (only the 16 is under the radical) √16

13. Special Circumstance Sometimes the denominator will not be a perfect square and you will have to use rules for changing fractions to take away the radical. 63 √7

14. Uh oh… There is a fraction in the radical! Simplify Since the fraction doesn’t reduce, split the radical up. How do I get rid of the radical in the denominator? Multiply by the “fancy one” to make the denominator a perfect square!

15. Simplify. Divide the radicals. Uh oh… There is a radical in the denominator! Whew! It simplified!

16. Simplify Uh oh… Another radical in the denominator!

17. Partners 48 √12

18. Assessment Prompt • How could you rewrite the following problems to make them easier to solve? √16(25) √64 √4 What are two other forms of this radical? √y2

19. Simplifying multiplication under a radical: You can multiply the radicals first and then simplify or you can simplify each radical then multiply: Ex: √8*4 = 4√2 or √4*16 = √4 * √16 = 2*4=8 Simplifying division under a radical: First you must determine what is under the radical: Ex: √49/25, √16 / 2, 24/√64 If the whole problem is under the radical, you simplify or divide first. If only one part is under the radical, you must simplify that part first. Simplifying addition or subtraction under a radical: You must solve the problem as is. Ex: √(4+16) = √20 or √4 + √16 = 6 You are finished simplifying when: The radicand cannot be simplified further There are no fractions under a radical. There are no radicals in your denominator. The square root of a square # is the #.

20. Simplifying Addition/Subtraction Expressions √ 4 + 16 √(42-6) √(5+20) √20 + √5 Do the last two problems have the same answer? What can you conclude about the way you have to simplify addition expressions?

21. Error Analysis √49 + √64 = √(49+64) = √113 ≈ 10.63

22. Tic-Tac-Think: Simplifying Radical Expressions: Choose 3 questions that will total at least 5 points 1 1 1 2 2 2 3 3 3