Practice 9-1. The Real Numbers. Write all names that apply to each number

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1 Chapter 9 Practice 9-1 The Real Numbers Write all names that apply to each number State if the number is rational, irrational, or not a real number

2 Find a real number between each pair of numbers and and and Give an example of an irrational number that is greater than Give an example of a number that is not real. 26. Give an example of a rational number between 1 2 and Give an example of a rational number between 4 and Give an example of an irrational number less than 0.

3 Chapter 9 Practice 9-1B The Real Numbers Write all names that apply to each number / ( 9)/ / (25/5) State if the number is rational, irrational, or not a real number (-5) / / (2/3)

4 Find a real number between each pair of numbers and and /5 and 2/5 24. Give an example of a number that is not real. 25. Give an example of a rational number between 1 2 and Give an example of a rational number between 2 and - 3

7 EJMS Mathematics Name ID: 1 A X2U0i1o6d `KduYtbaM ISwoMf\tjwba[rGe\ PLMLLCk.L G ganltlf vrqiqg^hpt`sj QrteUsMeHravzeydN. Practice 9-2 Use the Pythagorean Theorem to tind the missing length to the nearest tenth. Date Period 1) 2) ) 4) ) 6) K G2o0l1t6k fk^ujtbax YSfoNf_tmw_aJrpeB LLMLCCo.y w [Atlmlo [railgwhgtcsj OrkedsIeQryvreod^.l W KMHalddem sweivtzhw ai^nzfliknsintneq epnr\ey-yanlqgjeybcr`at. -1- Worksheet by Kuta Software LLC

8 7) 8) ) 10) ) 12) ) a = 8, b =?, c = ) a = 8.3, b = 4.2, c =? 15) a = 6.7, b =?, c = ) a =?, b = 3.1, c = 9.4 A X2S0K1^6M SKyuxtQaO YSDodfCttwzaXryeg elvlmcj.q m DAvlplH xrmidgohqtzsq crcegsaezrwvveedk.k i smvaidwe\ VwQiMtzh_ UIGnnfdipnniItxeh XPJrze`-gA_lEgeekbIrsaa. -2- Worksheet by Kuta Software LLC

9 EJMS Mathematics Name ID: 1 Q I2H0l1\7g KKnuat`av YSYoEfvt_wbacrXeL ZLFLWCR.E F haelilc trwiegmhrtvsw nrcershezrvvleld]. Practice 9-2B Use the Pythagorean Theorem to tind the missing length to the nearest tenth. Date Period 1) 2) ) 4) ) 6) L _2l0W1k7\ xkfurtuau xsyoof_ttwda^rber zlildcd.m i FAHltl^ Yrpi]gRhstcsJ mrmeysqekryvzeyd_.e K xmea]d`eo AwkiVt^hK WINnXfaiqn[iEtEeI lpernem-earlzgbedbvreag. -1- Worksheet by Kuta Software LLC

10 7) 8) ) 10) ) 12) ) a = 10.7, b = 8.9, c =? 14) a = 3.2, b = 7.9, c =? 15) a =?, b = 2.2, c = ) a = 5.1, b = 2, c =? U c2d0y1f7k kkku^toau escomfxtpwyaxrxeg oluljct.w f qaplmle kr^irgnhvtyst broensgefrav\eydu.o K RMcaZdeee cwkigt`h_ GIAnXfOifn\iFt^eE ap_rpek-fahlngqe[bmrrao. -2- Worksheet by Kuta Software LLC

11 Name Date Class Chapter 9 Lesson 9-1 Problem Solving The Real Numbers Write the correct answer. 1. Twin primes are prime numbers that differ by 2. Find an irrational number between twin primes 5 and Rounded to the nearest ten-thousandth, Find a rational number between 3 and. 3. One famous irrational number is e. Rounded to the nearest ten-thousandth e Find a rational number that is between 2 and e. 4. Perfect numbers are those for which the divisors of the number sum to the number itself. The number 6 is a perfect number because The number 28 is also a perfect number. Find an irrational number between 6 and Which is an integer? A the number half-way between 6 and 7 B the money in an account if the balance was $ and $21.87 was deposited C the net yardage after plays that resulted in a 15 yard loss, 10 yard gain, 6 yard gain and 5 yard loss 6. Which is an irrational number? A a number that can be expressed as a fraction B the length of a side of a square with area 2 cm 2 C the square root of a negative number

12 Name Date Class Chapter 9 Lesson 9-2 Problem Solving The Pythagorean Theorem Write the correct answer. Round to the nearest tenth. The first one is done for you. 1. A right triangle is 10 m and 3 m wide. How long is the hypotenuse? 2. A 12 foot-ladder is resting against a wall. The base of the ladder is 5 feet from the wall. How high up the wall will the ladder reach? 3. A square is 90 ft. on each side. How long is the diagonal? 4. A field is 100 yards long and 45 yards wide. Find the length of the diagonal of the field. 5. The diagonal of a square is 28 inches long. What is the perimeter of this square? 6. The piece of glass for a window is 3 feet wide. Its diagonal measures 8 feet. How tall is the piece of glass? Round to the nearest tenth. 7. A television screen measures approximately 15.5 in. high and 19.5 in. wide. In advertising, the approximate length of the diagonal of the screen is used. How should this television be advertised? 8. A wheelchair ramp that is constructed to rise 1 foot off the ground must extend 12 feet along the ground. How long is the actual ramp? Round to the nearest tenth.

13 Name Date Class Chapter 9 Practice 9-3 Applying the Pythagorean Theorem and its Converse 1. The length of a rectangular swimming pool is 50 feet. The width of the pool is 20 feet. What is the length of the diagonal of the pool? Round your answer to the nearest tenth. (hint: sketch a picture.) 2. A map is placed on a coordinate grid. Cincinnati located at (5, 4) and San Diego is located at ( 10, 3). How far apart is Cincinnati from San Diego on the map? Round your answer to the nearest tenth. (hint: Use Distance Formula) 3. Katie, Ralph, and Juan are tossing a football. Katie is 22.5 feet away from Ralph. Ralph is 58.5 feet away from Juan. Juan is 54 feet away from Katie. Do the distances between Katie, Ralph, and Juan form a right triangle? Explain. (hint: sketch a picture) 4. A rectangular picture from has a length of 7 inches and a width of 5 inches. What is the length of the diagonal of the picture frame? Round your answer to the nearest tenth. (hint: Sketch a picture)

14 Name Date Class Find the distance between the two points to the nearest tenth. (sketch a picture, if necessary) 5. (0, 5) and ( 4, 2) 6. (1, 9) and (6, 3) 7. ( 6, 4) and (2, 6) 8. ( 1, 7) and ( 3, 5) 9. (4, 0) and ( 9, 7) 10. (0, 8) and (4, 0) Tell whether the given side lengths form a right triangle , 24, , 40, , 28.8, , 15, , 36, , 6, 6.5

15 Name Date Class Chapter 9 Practice 9-3B Applying the Pythagorean Theorem and its Converse 1. The length of a rectangular swimming pool is 30 feet. The width of the pool is 15 feet. What is the length of the diagonal of the pool? Round your answer to the nearest tenth. (hint: sketch a picture, if necessary.) 2. A city map is placed on a coordinate grid. The bakery is located at (-2, 4). The bank is located at (4, -3) How far apart are the bakery and bank on the map? Round your answer to the nearest tenth. (hint: Use Distance Formula) 3. A triangular flag has side lengths of 14 in, 18 in. and 24 in. Is this flag a right triangle? Explain. (hint: sketch a picture) 4. A rectangular picture from has a length of 6 inches and a width of 10 inches. What is the length of the diagonal of the picture frame? Round your answer to the nearest tenth. (hint: Sketch a picture)

16 Name Date Class Find the distance between the two points to the nearest tenth. (sketch a picture, if necessary) 5. (1, 5) and ( 6, 2) 6. (2, 9) and (6, 8) 7. ( 3, 4) and (2, 9) 8. ( 1, 7) and ( 3, 5) 9. (4, 0) and ( 9, 7) 10. (0, 8) and (4, 0) Tell whether the given side lengths form a right triangle , 16, , 20, , 14.2, , 16, , 22, , 6, 9

17 Name Date Class Chapter 9 Lesson 9-3 Problem Solving Applying the Pythagorean Theorem and its Converse Solve each problem. 1. Linda made triangular flags for the spirit club to wave. Each flag was a right triangle. One side was 1.5 feet long and another side was 2.2 feet long. She used fringed trim along the longest side of the each flag. What was the length of fringed trim that she sewed to each flag? Round to the nearest tenth of a foot. 2. A wheelchair ramp starts 8 meters from the base of a staircase. The staircase is 1 meter high. What is the length of the wheelchair ramp? Round to the nearest tenth of a meter. 3. The city of Chicago is located at (4, 8) on a grid. The city of Memphis is located at (6, 12) on the grid. How many units apart are Chicago and Memphis on the grid? Round to the nearest tenth of a unit. 4. Tony needs to use a ladder to get onto the roof. The height of the house is about 11 feet. The ladder will be placed 6 feet from the house. What is the minimum height, to the nearest foot, that the ladder can be to safely reach the roof of the house?

18 Name Date Class Solve each problem. 5. An airplane is 33 miles due south and 56 miles due west of its destination airport. How far is the plane from the destination airport? 6. The location of a post office is marked at (2, 2) on a coordinate grid. To the nearest tenth, how far is the post office from the origin. 7. A rectangular tabletop has a length of 3.3 feet and a width of 8.8 feet. Which is the length of its diagonal to the nearest tenth? 8.The location of three ships are shown on a coordinate grid by the following points: X(0, 7), Y( 5, 3), and Z(4, 1). Which ships are farthest apart?

19 Chapter 9 Practice 9-4 Adding and Subtracting Radicals Simplify by adding or subtracting radicals, if possible

CCM8 Unit 7: Pythagorean Theorem Vocabulary

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