1. Squares and Square Roots 4-5 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. Squares and Square Roots 4-5 Warm Up Simplify. 25 64 144 225 400 1. 5 2 2. 8 2 3. 12 2 4. 15 2 5. 20 2

3. Squares and Square Roots 4-5 Problem of the Day A Shakespearean sonnet is a poem made up of 3 quatrains (4 lines each), and a couplet (2 lines). Each line is in iambic pentameter (which means it has 5 iambic feet). So, how many iambic feet long is a Shakespearean sonnet? 70

4. Squares and Square Roots 4-5 MA.8.A.6.2 Make reaonable approximations of square roots…,and use them to estimate solutions to problems… Sunshine State Standards

5. Squares and Square Roots 4-5 Vocabulary square root principal square root perfect square

6. Squares and Square Roots 4-5 Think about the relationship between the area of a square and the length of one of its sides. A number that when multiplied by itself to form a product is the square root of that product. Taking the square root of a number is the inverse of squaring the number. area = 36 square units side length = 6 units because 6 2 = 36 6 2 = 36 36 = 6

7. Squares and Square Roots 4-5 The numbers 16, 36, and 49 are examples of perfect squares. A perfect square is a number that has integers as its square roots. Other perfect squares include 1, 4, 9, 25, 64, and 81. Every positive number has two square roots, one positive and one negative. The radical symbol indicates the nonnegative or principal square root. The symbol – is used to indicate the negative square root. –49 is not the same as – 49. A negative number has no real square root. Caution!

8. Squares and Square Roots 4-5 Additional Example: 1 Finding the Positive and Negative Square Roots of a Number Find the two square roots of each number. 7 is a square root, since 7 7 = 49. –7 is also a square root, since –7 –7 = 49. 10 is a square root, since 10 10 = 100. –10 is also a square root, since –10 –10 = 100. 49 = –7 – 49 = 7 100 = 10 100 = –10 – A. 49 B. 100 C. 225 15 is a square root, since 15 15 = 225. 225 = 15 225 = –15 – –15 is also a square root, since –15 –15 = 225.

9. Squares and Square Roots 4-5 A. 81 Check It Out: Example 1 Find the two square roots of each number. B. 144 C. 324 9 9 = 81 81 = (–9)(–9) = 81 = ±9 12 12 = 144 144 = (–12)(–12) = 144 = ±12 18 18 = 324 324 = (–18)(–18) = 324 = ±18

10. Squares and Square Roots 4-5 13 2 = 169 Use the positive square root; a negative length has no meaning. The window is 13 inches wide. Write and solve an equation to find the area of the window. Additional Example 2: Application A square window has an area of 169 square inches. How wide is the window? So 169 = 13. The area of a square is s 2, where s is the length of a side. Remember!

11. Squares and Square Roots 4-5 Check It Out: Example 2 A square window has an area of 225 square inches. How wide is the window? The window is 15 inches wide. 225 = 15; 15 2 = 225 so

12. Squares and Square Roots 4-5 Additional Example 3A: Evaluating Expressions Involving Square Roots Simplify the expression. Evaluate the square root. Add. = 25 Multiply. = 18 + 7 3 36 + 7 3 36 + 7 = 3(6) + 7

13. Squares and Square Roots 4-5 Additional Example 3B: Evaluating Expressions Involving Square Roots Simplify the expression. + 25 16 3434 3434 + 3434 = + 1.5625 Evaluate the square roots. = 1.25 + 3434 25 16 = 1.5625. = 2 Add.

14. Squares and Square Roots 4-5 Check It Out: Example 3A Simplify each expression. 2 121 + 9 = 31 = 22 + 9 2 121 + 9 = 2(11) + 9

15. Squares and Square Roots 4-5 Check It Out: Example 3B Simplify each expression. + 16 36 2323 2323 + 4646 2323 = + 16 = + 2323 =, or 1 1313 36 4343

16. Squares and Square Roots 4-5 Check It Out: Example 3C Simplify each expression. –5 336 + 25 = –95 = –5(19) –5 336 + 25 = –5 361

17. Squares and Square Roots 4-5 Check It Out: Example 3D Simplify each expression. 12 2 48 = 48 = 12 = 2 48 2 48 12 2 576 = 2(24)

18. Squares and Square Roots 4-5 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

19. Squares and Square Roots 4-5 Lesson Quiz Find the two square roots of each number. 1. 81 2. 2500 Evaluate each expression. 3. 3 16 + 1 4. 7 9 – 2 49 9950 13 7 5. Ms. Estefan wants to put a fence around 3 sides of a square garden that has an area of 225 ft 2. How much fencing does she need? 45 ft

20. Squares and Square Roots 4-5 1. Find two square roots of each number. 64 A. 4 B. 8 C. 9 D. 16 Lesson Quiz for Student Response Systems

21. Squares and Square Roots 4-5 2. Find two square roots of each number. 6400 A. 4 B. 8 C. 80 D. 800 Lesson Quiz for Student Response Systems

22. Squares and Square Roots 4-5 3. Evaluate the expression. A. 44 B. 17 C. 19 D. 72 Lesson Quiz for Student Response Systems

23. Squares and Square Roots 4-5 4. Evaluate the expression. A. 4 B. 8 C. 16 D. 40 Lesson Quiz for Student Response Systems