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Square Root Conversion Tables

How to convert an integer to its square root using the tables below:

1)  Find a value in the column labeled X.

2)  The square root of that integer is beside X in the middle column labeled √ X.

3)  The third column is X2 and is the result of ( X ) • ( X ).

X

X

X2

X3

1

1

1

1

2

1.4142135

4

8

3

1.7320508

9

27

4

2

16

64

5

2.2360679

25

125

6

2.4494897

36

216

7

2.6457513

49

343

8

2.8284271

64

512

9

3

81

729

10

3.1622776

100

1,000

11

3.3166247

121

1,331

12

3.4641016

144

1,728

13

3.6055512

169

2,197

14

3.7416573

196

2,744

15

3.8729833

225

3,375

16

4

256

4,096

17

4.1231056

289

4,913

18

4.2426406

324

5,832

19

4.3588989

361

6,859

20

4.4721359

400

8,000

21

4.5825756

441

9,261

22

4.6904157

484

10,648

23

4.7958315

529

12,167

24

4.8989794

576

13,824

25

5

625

15,625

26

5.0990195

676

17,576

27

5.1961524

729

19,683

28

5.2915026

784

21,952

29

5.3851648

841

24,389

30

5.4772255

900

27,000

31

5.5677643

961

29,791

32

5.6568542

1,024

32,768

33

5.7445626

1,089

35,937

34

5.8309518

1,156

39,304

35

5.9160797

1,225

42,875

36

6

1,296

46,656

37

6.0827625

1,369

50,653

38

6.164414

1,444

54,872

39

6.2449979

1,521

59,319

40

6.3245553

1,600

64,000

41

6.4031242

1,681

68,921

42

6.4807406

1,764

74,088

43

6.5574385

1,849

79,507

44

6.6332495

1,936

85,184

45

6.7082039

2,025

91,125

46

6.7823299

2,116

97,336

47

6.8556546

2,209

103,823

48

6.9282032

2,304

110,592

49

7

2,401

117,649

50

7.0710678

2,500

125,000

X

X

X2

X3

51

7.1414284

2,601

132,651

52

7.2111025

2,704

140,608

53

7.2801098

2,809

148,877

54

7.3484692

2,916

157,464

55

7.4161984

3,025

166,375

56

7.4833147

3,136

175,616

57

7.5498344

3,249

185,193

58

7.6157731

3,364

195,112

59

7.6811457

3,481

205,379

60

7.7459666

3,600

216,000

61

7.8102496

3,721

226,981

62

7.8740078

3,844

238,328

63

7.9372539

3,969

250,047

64

8

4,096

262,144

65

8.0622577

4,225

274,625

66

8.1240384

4,356

287,496

67

8.1853527

4,489

300,763

68

8.2462112

4,624

314,432

69

8.3066238

4,761

328,509

70

8.3666002

4,900

343,000

71

8.4261497

5,041

357,911

72

8.4852813

5,184

373,248

73

8.5440037

5,329

389,017

74

8.6023252

5,476

405,224

75

8.660254

5,625

421,875

76

8.7177978

5,776

438,976

77

8.7749643

5,929

456,533

78

8.8317608

6,084

474,552

79

8.8881944

6,241

493,039

80

8.9442719

6,400

512,000

81

9

6,561

531,441

82

9.0553851

6,724

551,368

83

9.1104335

6,889

571,787

84

9.1651513

7,056

592,704

85

9.2195444

7,225

614,125

86

9.2736184

7,396

636,056

87

9.327379

7,569

658,503

88

9.3808315

7,744

681,472

89

9.4339811

7,921

704,969

90

9.4868329

8,100

729,000

91

9.539392

8,281

753,571

92

9.591663

8,464

778,688

93

9.6436507

8,649

804,357

94

9.6953597

8,836

830,584

95

9.7467943

9,025

857,375

96

9.7979589

9,216

884,736

97

9.8488578

9,409

912,673

98

9.8994949

9,604

941,192

99

9.9498743

9,801

970,299

100

10

10,000

1,000,000

For any table value of X:

1)    X = √ X • √ X

2)    X equals √ X2

3)    X2 = ( X ) • ( X )

4)    X2 = √ X • √ X • √ X • √ X

X equals 56 in the following example:

(The square root of 56 is 7.4833147)

1)    56 = 7.4833147 • 7.4833147

2)    56 = √ 3,136

3)    3,136 = 56 • 56

4)    3,136 = 7.4833147 • 7.4833147 •                      7.4833147 • 7.4833147