The document is a lesson plan on square roots for 9th grade math students. It introduces square roots and perfect squares. It defines key terms like radical sign, square root, radical expression, and perfect square. It provides examples of evaluating square roots with and without a calculator and finding the side length of a square given its area. Students are guided through practice problems finding square roots and whole number approximations. The homework assigned is worksheet 9.1 from page 819 of their textbook.

1. Evaluate. 2. 9 2 Lesson 9.1 , For use with pages 469-474 1. 5 2 You will NEED a calculator from now to the end of the year!

2. Evaluate. 2. 9 2 Lesson 9.1 , For use with pages 469-474 1. 5 2 You will NEED a calculator from now to the end of the year! ANSWER 25 ANSWER 81

3. Square Roots 9.1 Day 1

4. Our goals in this lesson : To understand how to take (or find) the square root of a number To be identify perfect squares

5. Essential Questions What is the difference between an irrational number and a rational number? How are real numbers and the Pythagorean Theorem used in everyday life? What types of real-life situations could the Pythagorean Theorem or square roots apply to? Why?

6. Vocabulary Radical Sign The symbol for the square root Square root Of a number N is the number that when multiplied by itself gives the number N. 5 and -5 are the square roots of 25 because 5 2 =25 and (-5) 2 =25.

7. Square Roots Principal Square Root Negative Square Root Both Square Roots

8. Vocabulary Radical Expression An expression that involves a radical sign Perfect Square Is a number with an integer square root such as 9, 16 and 25. Square root of the number must be a whole number to be a perfect square. NO decimal!

9. Perfect Squares: Area of a square = s 2 Side Length of a Square 1 2 3 4 5 6 7 8 9 10 Area 1 4 9 16 25 36 49 64 81 100 These are all the perfect squares that are less than 100.

10. Try these examples Are these numbers perfect squares? A) 729 B) 864 1444 1521

11. Try these examples Are these numbers perfect squares? A) 729 Yes, 27 B) 864 No 1444 Yes, 38. 1521 Yes, 39. How do you know?

12. Square Roots You can use square roots to find the side or length of a square. Area is 144 sq. feet. What is the length of each side? (A = s 2 ) 12 feet

13. Square Roots You can use square roots to find the side or length of a square. Area is 144 sq. feet. What is the length of each side?

14. The area of this square is 225 cm 2 What is the length of each side?

15. The area of this square is 225 cm 2 What is the length of each side? 15 cm

16. EXAMPLE 1 Evaluating Square Roots a. 36 b. 64 – c. 4 25 d. 0.81

17. EXAMPLE 1 Evaluating Square Roots = 6 = –8 = 0.9 a. 36 b. 64 – c. 4 25 2 5 = d. 0.81

18. GUIDED PRACTICE for Examples 1 and 2 Find or approximate the square root to the nearest integer . 1. 4 2. 0

19. GUIDED PRACTICE for Examples 1 and 2 Find or approximate the square root to the nearest integer . 1. 4 2. 0 ANSWER 2 ANSWER 0

20. GUIDED PRACTICE for Examples 1 and 2 Find or approximate the square root to the nearest integer. 3. 36 – 4. 81 –

21. GUIDED PRACTICE for Examples 1 and 2 Find or approximate the square root to the nearest integer. 3. 36 – 4. 81 – ANSWER – 6 ANSWER – 9

22. EXAMPLE 3 Using a Calculator Evaluate the square root. Round to the nearest tenth , if necessary. SOLUTION Keystrokes Answer Display a. 56.25 – b. 8 c. 1256 – a. b. c.

23. EXAMPLE 3 Using a Calculator Evaluate the square root. Round to the nearest tenth , if necessary. SOLUTION Keystrokes Answer Display – 7.5 2.8 – 35.4 a. 56.25 – b. 8 c. 1256 – a. b. c.

24. Simplifying radicals = = =

25. Simplifying radicals = = =

26. Find two consecutive integers that each is between

27. Find two consecutive integers that each is between

28. Homework Worksheet 9.1 See page 819