MSM07G8_RESBK_Ch04_035-042.pe 1/30/06 1:21 PM Page 38 Name Date LESSON Class Reteach 4-5 Squares and Square Roots A perfect square has two identical factors. 25 5 5 52 or 25 (5) (5) (5)2 then 25 is a perfect square. Tell if the number is a perfect square. If yes, write its identical factors. 1. 121 112 or 2 3. 400 112 or 2 2. 200 112 or 2 25 5 and 25 5 Since 52 25 and also (5)2 25, both 5 and 5 are square roots of 25. The principal square root of 25 is 5: 25 5 Write the two square roots of each number. 9 4. 81 ⫺9 81 25 5. 625 ⫺25 625 13 6. 169 169 ⫺13 Write the principal square root of each number. 12 7. 144 80 8. 6400 9. 10,00 0 100 5100 3 5(10) 3 50 3 47 Use the principal square root when evaluating an expression. For the order of operations, do square root first, as you would an exponent. Complete to evaluate each expression. 10. 3144 20 12 3 36 20 20 11. 25 144 13 169 13 16 13 13 26 12. ᎏ ᎏᎏ 2 25 1 100 100 1 ᎏ ᎏᎏ 2 25 10 ᎏᎏ ᎏ1ᎏ 2 5 2 1 ᎏ2ᎏ 1 2ᎏ2ᎏ Copyright © by Holt, Rinehart and Winston. All rights reserved. 38 Holt Mathematics Practice B 4-5 Squares and Square Roots Practice A 4-5 Squares and Square Roots LESSON LESSON Find the two square roots of each number. Find the two square roots of each number. 1. 16 2. 49 4, 4 5. 100 3. 1 7, 7 1, 1 6. 4 2, 2 8, 8 3 13. 36 10 1 16 64 10 18. 59 2 19. 100 15 17. 20. 381 16. 121 16 5 100 25 3 27 5 18. 5 15. 100 25 30 25 1 4 2 12. 73 48 10 14. 36 36 26 13 4 12, 12 11. 64 36 9 13. 264 10 16. 16 9 5 10. 100 19 7 6 15. 49 4 8. 144 5, 5 Evaluate each expression. 12. 31 5 4 14. 15 25 16 17. 11. 18 2 10, 10 7. 25 11, 11 9. 32 17 10. 7 6 4. 100 7, 7 6. 121 8, 8 Evaluate each expression. 9. 8 1 3. 49 9, 9 5. 64 8. 64 9, 9 2. 81 6, 6 5, 5 7. 81 10, 10 1. 36 4. 25 19. 27 196 49 2 6) 20. 3(144 2 18 The Pyramids of Egypt are often called the first wonder of the world. This group of pyramids consists of Menkaura, Khufu, and Khafra. The largest of these is Khufu, sometimes called Cheops. During this time in history, each monarch had his own pyramid built to bury his mummified body. Cheops was a king of Egypt in the early 26th century B.C. His pyramid’s original height is estimated to have been 482 ft. It is now approximately 450 ft. The estimated completion date of this structure was 2660 B.C. Switzerland’s flag is a square, unlike other flags that are rectangular. 21. If the flag of Switzerland has an area of 81 ft2, what is the length of each of its sides? (Hint: s A ) 9 ft 21. If the area of the base of Cheops’ pyramid is 570,025 ft2, what is the length of one of the sides of the ancient structure? (Hint: s A ) 22. If the lengths of the sides of a Switzerland flag are 10 ft, what is the area of the flag? (Hint: A s 2) 755 ft 100 ft2 22. If a replica of the pyramid were built with a base area of 625 in2, what would be the length of each side? (Hint: s A ) 25 in. 35 Copyright © by Holt, Rinehart and Winston. All rights reserved. Holt Mathematics LESSON Find the two square roots of each number. 2. 576 15, 15 5. 400 A perfect square has two identical factors. 3. 361 24, 24 25 5 5 52 or 25 (5) (5) (5)2 then 25 is a perfect square. 4. 625 19, 19 6. 729 7. 1024 25, 25 Tell if the number is a perfect square. If yes, write its identical factors. 8. 2500 112 or (11)2 1. 121 20, 20 27, 27 32, 32 50, 50 9 1 10. 4 144 1 2 13. 324 81 11. 6 14. 64 12. 100 16. ( 144 20 or (20) 64) 96 36 25 5 and 25 5 Write the two square roots of each number. 9 4. 81 7 not a perfect square The principal square root of 25 is 5: 25 5 7 15. 6( 225 9) 2. 200 2 Since 52 25 and also (5)2 25, both 5 and 5 are square roots of 25. 4 4 5 196 49 3 4 3 16 2 3. 400 Evaluate each expression. 9. Holt Mathematics Reteach 4-5 Squares and Square Roots Practice C 4-5 Squares and Square Roots LESSON 1. 225 36 Copyright © by Holt, Rinehart and Winston. All rights reserved. 9 81 25 5. 625 13 6. 169 25 625 169 13 Evaluate each expression. 17. 2 4 36 144 18. 676 15 8 Write the principal square root of each number. 19. 49 441 169 11 12 7. 144 41 20. The distance from base to base, home plate included, on a baseball field is 90 ft. The bases form a square. What is its area? 8100 ft2 9. 10,00 0 100 5100 3 5(10) 3 50 3 47 Complete to evaluate each expression. Switzerland’s flag is a square, unlike other flags that are rectangular. 10. 3144 20 21. Suppose a seamstress is making a flag that has to have an area less than 50 square meters. What is the longest length, to the nearest tenth, the sides can be? (Hint: s A ) 12 3 36 20 20 11. 25 144 13 169 13 16 13 13 26 12. 2 25 1 100 100 1 2 25 10 1 2 5 2 1 2 1 7.0 m Copyright © by Holt, Rinehart and Winston. All rights reserved. 80 8. 6400 Use the principal square root when evaluating an expression. For the order of operations, do square root first, as you would an exponent. 22 37 Copyright © by Holt, Rinehart and Winston. All rights reserved. Holt Mathematics Copyright © by Holt, Rinehart and Winston. All rights reserved. 76 38 Holt Mathematics Holt Mathematics

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