Square Roots and Cube Roots Unit 1 © Curriculum Associates, LLC Copying Is Not Permitted

Practice Lesson 2 Square Roots and Cube Roots Unit 1 © Curriculum Associates, LLC Copying is not permitted. 10? How do you know? you do How is n 5 10? n 5 120, s Roots Square Roots Cube and 32 1 d 5 58 represents the cost of the shoes. shoes. the of cost the represents much more money Alberto needs to save. How How save. to needs Alberto money more much save? to need he does more much I must find the amount that when added to 32 gives me 58. Because 1 26 5 58, I know Alberto needs to save another $26. 8 8 8 8 8 Challenge how nd ﬁ to equation your solve to how Explain equation the of side one that so equation an Write

s 4 5 8; The model shows a quantity divided into equal parts, and each part equals 8. No; Possible explanation: If n 5 10, the expression 10 equals 100, not 120. Possible answer: 6 x 5 42; Erika buys movie tickets. The total cost of the tickets is $42. What is the cost of each movie ticket? $7 solution because 6 ? 5 $42. Lesson 2 Lesson $58. He has already saved $32. He still needs to save save to needs still He $32. saved already has He $58. d dollars. equation? Explain know. you how equation? a real-world Write multiplication. and uses variable, equation. your with represent could you problem that solution. the 7 is that know you how Show C cost that shoes of a pair buy to money saving is Alberto the is What equation. a division illustrates model bar The 10 equation the In a includes 7, of a solution has that equation an Write 4 5 6 7 Solve. b. a. 14 14 C B M M

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You multiply 3 multiply You get 24. 8 to by Lesson 2 Lesson Name: 24 p p p p p 5 24 p 3 3 p 5 24? The variable p represents the number of photos on each page of the album. p equals 8. more than; Possible explanation: 36 > 24, so there would be more than 8 photos on each album page. Example has page Each photos. with pages 3 album filled has Isabella Write photos. 24 has Isabella photos. of number same the one on are photos many find how to equation an solve and album page. the represent to a variable Choose on onenumber of page. photos the describe to expression an Write pages. the on photos of number total the compare to equation an Write photos of number the and expression Isabella has. represent to model a bar Draw the equation. onThere one 8 are photos album page. problem? of number the Is pages. the between divided evenly she the than less or more pages these of one on photos number on one page in the example problem? Explain.number on one page in example the problem? in example the p represent variable the does What 3 equation the to solution the is What which photos 36 with pages 3 more lled ﬁ Isabella Then 1 2 3 Lesson 2 Square Roots and Cube Roots Square Roots and Cube Equations Understand Solutions to Prerequisite: solve and write to how problem showing the example Study 1–7. problems solve Then equation. an © Curriculum Associates, LLC Copying is not permitted. B B M

Practice and Problem Solving Unit 1 Expressions and Equations (Exponents) and the Number System 5 ©Curriculum Associates, LLC Copying is not permitted. Practice Lesson 2 Square Roots and Cube Roots Unit 1

3 ?

5 6, 6 in.; or

2 216 ···· ) ( 3 4

3 Ï 22 8

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2 512, or 512 in. 512 or 5 512, 296 in. 5 296 3 3 64

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22 ? The volume of Cube B is 296 cubic inches greater than the A.

8 216 in. 2 216

3 2 2 2 2 2 2 Roots Square Roots Cube and 2 Show the prime factors as 3 equal groups of 2 factors. of groups 3 equal as factors prime the Show ( the prime factorization Complete of 64. What is . A: length edge of Cube of in. 512 5 8 in. 1 6 in. 2 in. B: length edge of Cube of 8 B volume: Cube No; Possible explanation: The prime factorization of 48 is 2 • 3. I cannot make 3 equal groups of factors. Possible explanation: A cube root is a number multiplied together three times to get the original number. A square root is a number multiplied by itself to get the Lesson 2 Lesson than the length of each edge in Cube A. How much greater is the volume of Cube B than the the B than Cube of volume the is greater much A. How Cube in edge each of length the than A? Cube of volume work. your Show Solution: Is 48 a perfect Explain cube? your reasoning. root. a square from erent diff is root a cube how Explain longer 2 inches B is Cube in edge each of length The inches. cubic 216 A is Cube of volume The You can use prime factorization to fi root. a cube nd fi to factorization prime use can You 6 7 8 5 Solve. b a. c. 16 16 C M M M 15 15 the the 5 2

any number number any 5 27 8 ·· 3

3 3 Ï Vocabulary 3 27 is a perfect is 27 cube. cube root root cube multiplied is that to times three together number. original get the 2 is the cube root of 8. of root cube the 2 is perfect cube product integer an of together multiplied three times. x x Roots Square Roots Cube and Lesson 2 Lesson x Volume 5 343 cm Name: . . What is the length of each each of length the is . What 3 centimeters long. The of the volume centimeters x Simplify. Write the formula. Write . What is the length of each edge of the cube? the of edge each of length the is . What 3

343 343 343. of root cube the Find ····

3 Ï 7 5 5 343 5 343 V for 343 x for b and Substitute 5 V 3 3 The volume is the cube of length an edge. The length of an edge is the cube root volume. Each edge of the cube is 2 feet long. Possible explanation: A cube is the product of three identical factors. A cube root is the factor that is used three times to get a cube. x cube is 343 cm 343 is cube x Each edge of a cube is is a cube of edge Each a cube. of volume the for formula the Use x x long. 7 centimeters is cube the of edge Each Example edge length? volume? its to root. a cube is that a number and edge of the cube? the of edge What is the relationship of the volume of the cube to its its to cube the of volume the of relationship the is What cube the of length edge the of relationship the is What 8 ft is a cube of volume The a cube is that a number between erence diﬀ the Explain 1 2 3 4 Lesson 2 Find Cube Roots Cube Find find to a cube how problem showing the example Study 1–8. problems root. solve Then © Curriculum Associates, LLC Copying is not permitted. B B M M

6 Practice and Problem Solving Unit 1 Expressions and Equations (Exponents) and the Number System ©Curriculum Associates, LLC Copying is not permitted. Practice Lesson 2 Square Roots and Cube Roots Unit 1 8 ft 8 ft 1 8 x x x © Curriculum Associates, LLC Copying is not permitted.

. How long 3 2 d 4 16 5 t

243, or 243 cm 243 or 5 243, ; 9 • 27 13, or 13 ft 13 or 5 13, 2 3

3, so the length of each side is 3 cm; the so 3 cm; length is 5 3, side each of

1 8 169 ···· 2 2 2 9 ·· 2 2 2 Ï Ï 5 x 5 x The object takes 2 seconds to fall 64 feet. fall to 2 seconds object takes The The volume of the rectangular prism is 243 cubic centimeters. cubic 243 is the of rectangular prism volume The feet of railing. will need 21 Taylor 5 t 5 t 5 t 5 x

4 ·· , V 5 27 cm Roots Square Roots Cube and 3 Ï 2 8 5 9; s 5 2 ÷ 16 5 t d ÷ 16 2 64 ÷ 16 5 t 64 ÷ 16 4 seconds is given by the equation the equation by given is seconds V 5 3 s 169 x 5 Lesson 2 Lesson 21, or 21 ft 21 or 1 8 5 21, 13 railing: of Amount 233 233 Use 9 of these cubes to make a rectangular prism. What What prism. a rectangular make to cubes these 9 of Use prism? rectangular the of volume the is work. your Show Solution: area of the deck is 233 square feet. Taylor is going to put put to going is Taylor feet. square 233 is deck the of area of feet many How edge. longest the along a railing railing will she need? work. your Show Solution: t does it take a dropped object to fall 64 feet? fall to object a dropped take it does work. your Show Solution: centimeters. 9 square is a cube of face top the of area The deck. The of Taylor’s the dimensions The shows diagram in falls object a dropped that feet d in distance The 5 6 4 Solve. 18 18 C M M 17 17 5 100 square 2 Roots Square Roots Cube and 144. Lesson 2 Lesson Name: . 5 144 square inches, and 100 2 300 • 2 5 6005 300

. Is the area of the base of the cube greater than than greater cube the of base the of area the . Is 3 90,000 90,000. of 90,000 root square the Find ······ the formula. Write Ï 5 A 5 90,000 A 90,000 for Substitute 2 2 20 cm 60 meters Less than; The length of an edge is 10 in., so the area base inches. One square foot is 12 Markus walked 600 meters. walked Markus Example Markus walked halfway around a square park that has an area walk? Markus did meters many How meters. 90,000 square of of length find the to a square of area the for formula the Use halfway so find walked around, Markus one side. the total walked. he distance find the to park the of two sides of length s s The length of 2 sides 300 s 5 300 m. 300 is side each of length The s 5 meters. What is the length of one side of the park? park? the of side one of length the is What meters. in. 1,000 8,000 cubic centimeters of water. What is the length of of length the is What water. of centimeters 8,000 cubic an edge of the container? or less than 1 square foot? Explain. foot? 1 square than less or square 3,600 of area an has park square A smaller a full, cube-shaped hold When will completely container of a volume has a cube of shape the in A planter 1 2 3 Lesson 2 Solve Word Problems Solve Word square use to how problem showing the example Study solve problems. Then word solve to roots cube and roots problems 1–6. © Curriculum Associates, LLC Copying is not permitted. B B M

Practice and Problem Solving Unit 1 Expressions and Equations (Exponents) and the Number System 7 ©Curriculum Associates, LLC Copying is not permitted. Practice Lesson 2 Square Roots and Cube Roots Unit 1 ?

1 4 ·· Remember that a the is square What perfect square is the is square perfect of twoproduct equal factors. of theroot of numerator What is the is square What of theroot denominator? © Curriculum Associates, LLC Copying is not permitted. . 3 ft

1 8 ··

1 8 ·· 5

1 2

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1 x

1 2 The volume of the cube is the of is cube volume The ··

quare centimeters

1 3

2 2

1 4

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1 2 1 4 Ï ·· 1 1 ·· x . What is the volume of the cube? the of volume the is . What 125 square centimeters 125 square144 centimeters 102 s 121 s Roots Square Roots Cube and 2 5 5 5 ft 2

225 square centimeters 240 square centimeters 1 4 x V 5 x x V 5 V 5 x ·· D E F 250 square centimeters. Which could be the area of the the of area be the could Which centimeters. square 250 square? Selectsquare? all that apply. A B C Show your work. your Show Solution: and 100 between a perfect is square a square of area The is base the of area The shown. is a cube of base The Lesson 2 Lesson 4 5 Solve. 20 C 20 B 19 19 ? 2

x Roots Square Roots Cube and How do you find the Remember that a 3 ÷ 3? is What value of value the is cube perfect product of three equal factors. Lesson 2 Lesson Name: , 2 x 30 inches 30 900 inches No No No No 3 C D u u u u Yes Yes Yes Yes to tell whether the number is a is number the whether tell to 3 3 3 u u u u ? 3) 4 3 or No 2 2 The length of a side of the base is 5 inches. is length the of base a side The of b

is the length of where b is one of) 4 3, side the Yes is the length of one side. Find the length the of the Find the length of is one side. h 2 5 ( 5 b 5 b 5 b

b 5 inches 5 inches 25 inches 25 ··· 100 27 125 5 He multiplied 150 by 6 instead of dividing and then by He multiplied 150 900. of root the square found 25 Ï 25 perfect cube. a. where x b. c. d. 1,000 side of a cube with a surface area of 150 square inches. square 150 of area a surface with a cube of side A B get he did How answer. Jack correct chose the C as that answer? V 5 ( is the height of the pyramid. Find the the Find pyramid. the of square base height the and h is has that pyramid a square of base the of a side of length inches. cubic 25 of a volume and 3 inches of a height work. your Show Solution: S 5 6 is a cube of area surface the for formula The Choose is pyramid a square of volume the for formula The 1 2 3 Lesson 2 Square Roots Roots and Cube the problems.Solve © Curriculum Associates, LLC Copying is not permitted. B M M

8 Practice and Problem Solving Unit 1 Expressions and Equations (Exponents) and the Number System ©Curriculum Associates, LLC Copying is not permitted.