1. 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up Simplify. 1. 6 2 2. 7 2 3. 11 2 4. 15 2 36 49 121 Course 2 8-7 Squares and Square Roots 225

3. Problem of the Day The square of two whole numbers are 16 units apart on a number line. What are the two numbers? 3 and 5 Course 2 8-7 Squares and Square Roots

4. Learn to find and estimate square roots of numbers. Course 2 8-7 Squares and Square Roots

5. Vocabulary perfect square square root radical sign Insert Lesson Title Here Course 2 8-7 Squares and Square Roots

6. 2 Exponent Base A square with sides that measure 3 units each has an area of 3 · 3, or 3 2. Notice that the area of the square is represented by a power in which the base is the side length and the exponent is 2. A power in which the exponent is 2 is called a square. Course 2 8-7 Squares and Square Roots

7. Find each square. Additional Example 1A: Finding Squares of Numbers 12 2 Method 1: Use a Model A = lw A = 12 · 12 A = 144 The square of 12 is 144. 12 Course 2 8-7 Squares and Square Roots

8. Find each square. Additional Example 1B: Finding Squares of Numbers 3.5 2 Method 2: Use a Calculator Press 3.5. 3.5 2 = 12.25 The square of 3.5 is 12.25. Course 2 88-7 Squares and Square Roots x2x2 ENTER

9. Find each square. Check It Out: Example 1A 10 2 Method 1: Use a Model A = lw A = 10 · 10 A = 100 The square of 10 is 100. Course 2 8-7 Squares and Square Roots 10

10. Find each square. Check It Out: Example 1B 5.2 2 Method 2: Use a Calculator Press 5.2. 5.2 2 = 27.04 The square of 5.2 is 27.04. Course 2 8-7 Squares and Square Roots x2x2 ENTER

11. A perfect square is the square of a whole number. The number 49 is a perfect square because 49 =7 2 and 7 is a whole number. The number 6.25 is not a perfect square. The square root of a number is one of the two equal factors of the number. Four is a square root of 16 because 4 · 4 = 16. The symbol for a square root is √, which is called a radical sign. Course 2 8-7 Squares and Square Roots

12. √16 = 4 is read as “The square root of 16 is 4.” Reading Math Course 2 8-7 Squares and Square Roots

13. Find each square root. The square of 16 is 4. Course 2 8-7 Squares and Square Roots √16 Method 1: Use a Model Additional Example 2A: Finding Square Roots of Perfect Squares

14. Find each square root. Press 676. The square of 676 is 26. Course 2 8-7 Squares and Square Roots x2x2 ENTER Additional Example 2B: Finding Square Roots of Perfect Squares √676 Method 2: Use a Calculator 2nd √676 = 26

15. Check It Out: Example 2A The square of 25 is 5. Course 2 8-7 Squares and Square Roots Find each square root. √25 Method 1: Use a Model

16. Find each square root. √289 Method 2: Use a Calculator Press 289. The square of 289 is 17. Course 2 8-7 Squares and Square Roots x2x2 ENTER Check It Out: Example 2B 2nd √289 = 17

17. Estimate each square root to the nearest whole number. Use a calculator to check your answer. Additional Example 3A: Estimating Square Roots 36 < 40 < 49 Check Find the perfect squares nearest 40. Find the square roots of 36 and 49. 40 is closer in value to 36 than to 49. 6 is a reasonable estimate. √36 < √40 < 49 √ 6 < 40< 7 √ 40  6 √ 40  6.32455532033 √ Use a calculator to approximate √40. √40 Course 2 8-7 Squares and Square Roots

18. Additional Example 3B: Estimating Square Roots Estimate each square root to the nearest whole number. Use a calculator to check your answer. 64 < 79 < 81 Check Find the perfect squares nearest 79. Find the square roots of 64 and 81. 79 is closer in value to 81 than to 64. √79 79  9 √ 79  8.8881944 √ 8 < 79< 9 √ √64 < √79 < 81 √ Use a calculator to approximate √79. 9 is a reasonable estimate. Course 2 8-7 Squares and Square Roots

19. Check It Out: Example 3A Insert Lesson Title Here Estimate each square root to the nearest whole number. Use a calculator to check your answer. √22 16 < 22 < 25 Check Find the perfect squares nearest 22. Find the square roots of 16 and 25. 22 is closer in value to 25 than to 16. 4 < 22< 5 √ 22  5 √ 22  4.690415759 √ √16 < √22 < 25 √ Use a calculator to approximate√22. 5 is a reasonable estimate. Course 2 8-7 Squares and Square Roots

20. Check It Out: Example 3B Insert Lesson Title Here √53 49 < 53 < 64 Check Find the perfect squares nearest 53. Find the square roots of 49 and 64. 53 is closer in value to 49 than to 64. 7 < 53< 8 √ 53  7 √ 53  7.2801098828 √ √49 < √53 < 64 √ Use a calculator to approximate √53. Estimate each square root to the nearest whole number. Use a calculator to check your answer. 7 is a reasonable estimate. Course 2 8-7 Squares and Square Roots

21. A Coast Guard boat searching for a lost sailboat covers a square area of 125 mi 2. What is the approximate length of each side of the square area? Round your answer to the nearest mile. Additional Example 4: Recreation Application 121 < 125 < 144 Find the perfect squares nearest 125. Find the square roots of 121 and 144. Each side of the search area is about 11 miles long. 125 is closer to 121 than to 144. The length of each side of the square is √125. < < √125√121 √144 11 < < 12√125 √125  11 Course 2 8-7 Squares and Square Roots

22. Check It Out: Example 4 A tent was advertised in the newspaper as having an enclosed square area of 168 ft 2. What is the approximate length of the sides of the square area? Round your answer to the nearest foot. Insert Lesson Title Here The length of each side of the square is √168. 144 < 168 < 169Find the perfect squares nearest 168. Find the square roots of 144 and 169. < < √168√144 √169 12 < < 13√16 8 √168  13 Each side of the tent is about 13 feet long. 168 is closer to 169 than to 144. Course 2 8-7 Squares and Square Roots

23. Lesson Quiz Find each square. 1. 16 2 2. (3.5) 2 Estimate each square root to the nearest whole number. Use a calculator to check. 3. 5. A square dining room table has an area of 20 ft 2. What is the length of each side of the table, to the nearest tenth? 12.25 256 Insert Lesson Title Here 4 7 √15 4. √52 4.5 ft Course 2 8-7 Squares and Square Roots