Numerical roots and radicals pkt with answers

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Numerical Roots and Radicals Chapter Questions1. What are the properties of a square?2. What does taking the square root have to do with the area of a square?3. Why is it helpful to memorize perfect squares?4. What can be helpful when finding the square roots of numbers greater than 400?5. Why is it helpful to memorize perfect squares?6. Explain how to take the square root of a fraction or a decimal.7. Explain how to approximate a square root.8. What is the difference between an irrational and rational number?9. Why would we simplify a non-perfect square root instead of just estimating it?10. How do you solve an equation with perfect square and cube roots?

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Numerical Roots and Radicals Chapter Problems

Squares, Square Roots & Perfect SquaresClasswork1. A square has an area of 9 units2.

a. What is the side length of a square of this area?

b. Draw a square with an area of 9 units2.

c. What is the square root of 9?

d. Explain why your answers in parts (a) and (c) are the same.

2. Fill in the following table:

Side Lengthof a square

(units)

Area ofthe square

(units2)

1

2

3

4

5

6

7

8

9

10

11

12

13

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3. Explain how the table above helps you find the square root of 121?

4. Simplify each square root.a. √25b. √64c. √81d. √49e. √16

Homework

5. A square has an area of 36 units2.a. What is the side length of a square of this area?

b. Draw a square with an area of 36 units2.

c. What is the square root of 36?

d. Explain why your answers in parts (a) and (c) are the same.



(units)

Area of thesquare(units2)

14

15

16

17

18

19

20

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7. Simplify each square root.a. √289b. √400c. √196d. √361e. √144

Squares of Numbers Greater Than 20

Classwork



(units)


10

20

30

40

50

60

70

80

90

100

9. If you compare that to the table of side lengths from 1-10, what pattern do you notice?

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10. Simplify each square root.a. √2809b. √7921c. √484d. √6400e. √2025f. √225g. √841h. √9409i. √961j. √4356

Homework

11. Simplify each square root.a. √5041b. √1296c. √8464d. √3025e. √3721f. √6889g. √576h. √2401i. √2500j. √289

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Simplifying Perfect Square Radical ExpressionsClasswork

12. Simplify each square root.a. √25b. √64c. −√81d. √−81e. √49f.

g.

h.

i.

j. −k. √. 64l. √. 0081m. −√. 25n. √. 0016o. √−.04

Homework

13. Simplify each square root.a. √289b. -√400c. √64d. √361e. √−10000f.

g.

h.

i. -

j.

k. √−.09l. −√. 0196m. √. 49n. √. 0361o. √. 25

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Approximating Square RootsClasswork14. What two integers do the following square roots fall between?

a.b.c.d.e.

15. Draw and label a number line from 0 to 10. Place the following square roots on the number line.a.b.c.d.e.

16. Estimate the following square roots.a.b.c.d.e.f.g.h.i.j.

17. Approximate the square root to the nearest integer

a.

b.

c.

d.

e.

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a.b.c.d.e.




a.

b.

c.

d.

e.



a.b.c.d.e.




a.

b.

c.

d.

e.

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Homework18. What two integers do the following square roots fall between?

a.b.c.d.e.




a.

b.

c.

d.

e.



a.b.c.d.e.




a.

b.

c.

d.

e.



a.b.c.d.e.




a.

b.

c.

d.

e.

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Rational & Irrational NumbersClasswork22. Circle the numbers below that are rational

a. 3.5b. √6c. πd.

e. √10f. −√49g. √108h. 0.25i.

j. 0.4Homework23. Circle the numbers below that are irrational.

a.

b. √7c. √81d. 6.75e.f. √121g. √61h. πi. √225j. 0.18

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Radical Expressions Containing Variables

Classwork24. Simplify

a.

b.

c.

d.

e.

f.

g.

h.

Homework25. Simplify

a.

b.

c.

d.

e.

f.

g.

h.




a.

b.

c.

d.

e.

f.

g.

h.


a.

b.

c.

d.

e.

f.

g.

h.




a.

b.

c.

d.

e.

f.

g.

h.


a.

b.

c.

d.

e.

f.

g.

h.

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Simplifying Non-Perfect Squre RadicandsClasswork26. Simplify

a.b.c.d.e.f.g.h.i.j.

k.

l.

m.



k.

l.

m.




k.

l.

m.



k.

l.

m.




k.

l.

m.



k.

l.

m.

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Simplifying Roots of VariablesClasswork28. Simplify

a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

k.


a.

b.

c.

d.

e.

f.

g.

h.

i.



a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

k.


a.

b.

c.

d.

e.

f.

g.

h.

i.



a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

k.


a.

b.

c.

d.

e.

f.

g.

h.

i.

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Properties of ExponentsClasswork30. Complete each equation for the missing value:

a. (52)(55) = 5?

b. (127)(123) = 12?

c. (3-2)(35) = 3?

d. (49)(4-3) = 4?

e. (54)(5?) = 512

f. (107)(10?)(10-6) = 103

g. 34 ÷ 32 = 3?

h. = 5?

i. = 9?

j. 124 ÷ 126 = 12?

k. 108 ÷ 10? = 103

l. = 24

Homework31. Complete each equation for the missing value:

a. (122)(127) = 12?

b. (25)(22) = 2?

c. (5-3)(55) = 5?

d. (158)(15-5) = 15?

e. (67)(6?) = 615

f. (11-6)(11?)(118) = 115

g. 77 ÷ 73 = 7?

h. = 11?

i. 37 ÷ 39 = 3?

6

9

5

5

8

5

9

9

3

?

2

2

6

10

11

11

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j. = 2?

k. = 132

l. 5? ÷ 56 = 53

Solving Equations with Perfect Square and Cube RootsClasswork32. Solve.

a. 4 = 32b. = 28c. = −25d. 6 = 864e. 3 = 147

Homework33. Solve.

a. 21 = −21b. = 125c. 7 = 252d. −6 = 162e. = 4

10

6

2

2

?

6

13

13

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Numerical roots & Radicals Multiple choice Questions

Determine whether the given numbers are perfect squares. Circle your answer.

1) 1 Yes No

2) 8 Yes No

3) 16 Yes No

4) 25 Yes No

5) 82 Yes No

Circle the simplified version of each square root:

6) √144a. 14b. 12c. 72d. 21

7)

a. 10b. 6c. 0.6d. 18

8) −√. 0049a. -7b. 0.7c. 0.07d. -0.07

Circle whether the given number is rational or irrational9) π rational irrational10) 0.875 rational irrational11))√39 rational irrational

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Between what two integers do the following square roots fall?

12) √45a. 4 & 5b. 6 & 7c. 7 & 8d. 5 & 6

13)√125a. 11 & 12b. 12 & 13c. 13 & 14d. 14 & 15

14)Simplify: √45a. 40√5b. 2√5c. 3√5d. 9√5

15)(47)(43) = 4?

a. 10b. 24c. 4d. 5

Short Constructed Response – Write the correct answer for each question. No partial credit will begiven.

16) Approximate √47 ≈ ________

17) Approximate √230 ≈ ________

18) Solve: 5 2 = 180

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19) Solve:

20) 75 ___________________

21) ∶ 200 _____________________

22) Find the missing value 114 ÷ 116 = 11? ____________________

23) = ?________________

24) (67)(6-2) = 6?

25) Simplify √ ____________

1082

3

x

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Extended Constructed Response - Solve the problem, showing all work. Partial credit may be given.

26) Write two exponential expressions with like bases. Leave all answers in simplified exponential form.

a. Expression 1:

Expression 2:

b. Multiply your expressions.

c. Divide your expressions.

d. Raise your first expression to the 5th power.

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3 units

3 units

Answer Key

1.a. 3 unitsb.

c. 3d. Area of a Square = Side2 and 9 = 32

2.Side Lengthof a Square

(units)


1 1

2 4

3 9

4 16

5 25

6 36

7 49

8 64

9 81

10 100

11 121

12 144

13 169

3. Since Area of a square = side2, the square root of the area = side. So, √121 = 11.

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6 units

6 units

4.a. 5b. 8c. 9d. 7e. 4

5.a. 6 unitsb.

c. 6d. Area = Side2 and 36 = 62

6.Side Lengthof a square

(units)


14 196

15 225

16 256

17 289

18 324

19 361

20 400

7.a. 17b. 20c. 14d. 19e. 12

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8.Side Lengthof a square

(units)


10 100

20 400

30 900

40 1600

50 2500

60 3600

70 4900

80 6400

90 8100

100 10,000

9. Each answer in this table is 100 times greater than the corresponding answer in the other table. (or102 times greater).

10.a. 53b. 89c. 22d. 80e. 45f. 15g. 29h. 97i. 31j. 66

11.a. 71b. 36c. 92d. 55e. 61f. 83g. 24h. 49i. 50j. 17

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12.a. 5b. 8c. -9d. No real solutione. 7

f.

g. No real solutionh. ½

i.

j. – ½k. 0.8l. 0.09m. -0.5n. 0.04o. No real solution

13.a. 17b. -20c. 8d. 19e. No real solutionf. 1/3g. ½h. No real solutioni. -3/4j. 1/10k. No real solutionl. -0.14m. 0.7n. 0.19o. 0.5

14.a. 8 and 9b. 12 and 13c. 2 and 3d. 7 and 8e. 10 and 11

15.

5

7

5

7



f.


i.




15.



f.


i.




15.

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16.a. 2.45b. 8.37c. 7.42d. 3.74e. 10.29f. 6.4g. 8.94h. 8.06i. 2.83j. 15.26

17.a. 7b. 6c. 8d. 3e. 9


19.

20.a. 8.83b. 2.65c. 7.94d. 5.39e. 6.48f. 11.75g. 17.32h. 12.17i. 4.58j. 7.21

21.a. 4b. 6c. 4d. 6e. 7


16.a. 2.45b. 8.37c. 7.42d. 3.74e. 10.29f. 6.4g. 8.94h. 8.06i. 2.83j. 15.26

17.a. 7b. 6c. 8d. 3e. 9


19.

20.a. 8.83b. 2.65c. 7.94d. 5.39e. 6.48f. 11.75g. 17.32h. 12.17i. 4.58j. 7.21

21.a. 4b. 6c. 4d. 6e. 7


16.a. 2.45b. 8.37c. 7.42d. 3.74e. 10.29f. 6.4g. 8.94h. 8.06i. 2.83j. 15.26

17.a. 7b. 6c. 8d. 3e. 9


19.

20.a. 8.83b. 2.65c. 7.94d. 5.39e. 6.48f. 11.75g. 17.32h. 12.17i. 4.58j. 7.21

21.a. 4b. 6c. 4d. 6e. 7

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22.a. Rationalb. Irrationalc. Irrationald. Rationale. Irrationalf. Rationalg. Irrationalh. Rationali. Rationalj. Rational

23.a. Rationalb. Irrationalc. Rationald. Rationale. Rationalf. Rationalg. Irrationalh. Irrationali. Rationalj. Rational

24.a.

b.

c.

d.e.f.

g.h.

25.a.

b.c.

d.e.f.

g.

h.

3b b3b

b b2b b2b

b4b4b b

3x x2x x

x2x4x3x

x x4x x

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26.a. 5b. 4

c. 2

d. 2

e. 5

f. 10

g. 5

h. 2

i. 3

j. 6

k. 105

l. 33

m. 6627.

a. 4

b.

c.

d.

e.

f.

g.

h.i.

j.

k.

l.m.

28.a.

b.

c.

d.

e.

2

3

5

2

3

3

5

7

7

2

3

2

6

6

5 6

4 5

2 6

10 5

6 3

2 30

7 3

2 21

8 5

56 5

120 3

112 2

2 23 2x y z x4 41x y z z

2 3 30x y z y3 4 47 x y z yz

33 3x yz yz

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f.

g.

h.

i.

j.

k.29.

a.

b.

c.

d.

e.

f.

g.

h.

i.30.

a. 7b. 10c. 3d. 6e. 8f. 2g. 2h. 3i. -3j. -2k. 5l. 7

31.a. 9b. 7c. 2d. 3e. 8f. 3

2 2 42 7x y z y

2 42 14x y z x

3 35x y z x

yzyx 3133

2 3 4 58x y z xz

4 2 17x y z y

2 4 22 10x y z xz3 3 3x y z yz

2 3 22 6x y z

3 2 3 65x y z y

2 14x y z x2 2 3 10x y z yz

yzyzx 72 22

4 22x y z z

4 33 3x y z xy

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g. 4h. 4i. -2j. -4k. 4l. 9

32.a. 2b. ±14c. -5d. ±12e. ±7

33.a. -1b. ±25c. ±6d. -3e. 4

Review answers1. Yes2. No3. Yes4. Yes5. No6. B7. C8. D9. Irrational

10. rational11. irrational12. b13. a14. c15. a16. 717. 1518. 6

19. -620. 5x7y√321. 10xyz2√222. -223. 424. 525. x5

26. Expressions will vary

Numerical roots and radicals pkt with answers

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