SQUARE ROOTS BY LONG DIVISION METHOD

Square and square roots of Class 8

  • Obtain the number whose square root is to be computed.
  • Place bars over every pair of digits starting with unit digit. 

For example:

  • Think of the largest number whose square is less than or equal to the first pair. Take this number as the divisor and the quotient.
  • Put the quotient above the period and write the product of divisor and quotient just below the first period.
  • Subtract the product of quotient and divisor.
  • Bring down the second period on the right of the remainder. This is the new dividend.
  • Double the quotient and write this number on the left of the remainder as shown with a blank on the right for the next digit as the next possible divisor.
  • Enter a new digit to fill the blank and also as the new digit in the quotient such that the product of this new digit in the quotient with the new divisor is less than or equal to the new divisors.
  • Subtract and bring down the next period (if any).
  • Repeat the above two steps till all bars have been considered, the final quotient is the required square root.

e.g. Finding the square root of 40: 

SQUARE ROOTS BY LONG DIVISION METHOD

The answer is 6.324 . . . taking the method as far as three decimal places.
Notice the position of the decimal point and step away from there in both directions, two digits at a time. Each of those pairs will lead to one digit of the answer, and remember the zeros continue indefinitely. 

Start on the left. The first pair is 40. Find the largest square smaller than 40, that's 36. Subtract the 36 from the 40, which leaves 4, and enter a 6 as the first digit of your answer. 

Next take the 4 and 'bring down' the next pair of digits (00 as it happens) to make 400. We are trying to decide the second digit of our answer and we find it like this: 

Use the 6 but double it (12) and make that ten times bigger (120). Now find 'something'- a single digit, so that one hundred and twenty 'something' times that same 'something' is as large as possible but less than the 400. 

123 times 3 makes 369, so three is the digit we want (124 times 4 would have been too big). 

Subtract the 369 from the 400 (31) and 'bring down' the next pair of digits (so we are now aiming for 3100). The digits we have so far in the answer are 6 and 3. Double 63 and then make it ten times bigger (1260). Use the same technique as before: find one thousand two hundred and sixty 'something', times 'something', that gets as close as possible to 3100 without exceeding it. 

Our third digit will be 2, 1262 times 2 is 2524, 1263 times 3 would be too large. 

Subtract to leave 576, bring down the next pair of digits, double the digits you already have, that's 632, which doubles to make 1264, now look for twelve thousand, six hundred and forty 'something' times 'something' to come as close as possible to 57,600 without exceeding it. That 'something' is 4 (check it), and so we continue until we have as many digits in our answer as we think we need.

APPROXIMATE VALUES OF SQUARE ROOTS BY USING SQUARE ROOT TABLES:

In our practical problems, we need the square roots of numbers. Square roots of numbers by the method of long division is very time consuming and cumbersome. For this reason, tables have been prepared which provide the approximate values of square roots of different numbers correct to a certain decimal place.

The following table gives the values of square roots of all natural numbers from 1 to 99.

x

SQUARE ROOTS BY LONG DIVISION METHOD

x

SQUARE ROOTS BY LONG DIVISION METHOD

x

SQUARE ROOTS BY LONG DIVISION METHOD

x

SQUARE ROOTS BY LONG DIVISION METHOD

1

1.000

26

5.999

51

7.141

76

8.718

2

1.414

27

5.196

52

7.211

77

8.775

3

1.732

28

5.292

53

7.208

78

8.832

4

2.000

29

5.385

54

7.348

79

8.888

5

2.236

30

5.447

55

7.416

80

8.944

6

2.449

31

5.568

56

7.483

81

9.000

7

2.646

32

5.657

57

7.550

82

9.055

8

2.828

33

5.745

58

7.616

83

9.110

9

3.000

34

5.831

59

7.681

84

9.165

10

3.162

35

5.916

60

7.746

85

9.220

11

3.317

36

6.000

61

7.810

86

9.274

12

3.464

37

6.083

62

7.874

87

9.327

13

3.606

38

6.164

63

7.937

88

9.381

14

3.742

39

6.245

64

8.000

89

9.434

15

3.873

40

6.325

65

8.062

90

9.487

16

4.000

41

6.403

66

8.124

91

9.539

17

4.123

42

6.481

67

8.185

92

9.592

18

4.243

43

6.557

68

8.246

93

9.644

19

4.359

44

6.633

69

8.307

94

9.695

20

4.472

45

6.708

70

8.367

95

9.747

21

4.583

46

6.782

71

8.426

96

9.798

22

4.690

47

6.856

72

8.485

97

9.849

23

4.796

48

6.928

73

8.544

98

9.899

24

4.899

49

7.000

74

8.602

99

9.950

25

5.009

50

7.071

75

8.660

   

CBSE NCERT Solutions for Class 8 Maths

class 8 maths NCERT solutions Chapter 1: Rational Numbers

class 8 maths NCERT solutions  Chapter 2: Linear Equations in One Variable

class 8 maths NCERT solutions  Chapter 3: Understanding Quadrilaterals

class 8 maths NCERT solutions Chapter 4: Practical Geometry

class 8 maths NCERT solutions  Chapter 5: Data Handling

class 8 maths NCERT solutions  Chapter 6: Square and Square Roots

class 8 maths NCERT solutions  Chapter 7: Cube and Cube Roots

class 8 maths NCERT solutions  Chapter 8: Comparing Quantities

NCERT Class 8 Maths solution Chapter 9: Algebraic Expressions and Identities

class 8 maths NCERT solutions  Chapter 10: Visualizing Solid Shapes

class 8 maths NCERT solutions Chapter 11: Mensuration

class 8 maths NCERT solutions  Chapter 12: Exponents and Powers

class 8 maths NCERT solutions  Chapter 13: Direct and Inverse Proportions

class 8 maths NCERT solutions  Chapter 14: Factorization

class 8 maths NCERT solutions  Chapter 15: Introduction to Graphs

class 8 maths NCERT solutions  Chapter 16: Playing with Numbers

Notes,worksheet and solved question for Maths class 8 

  1.  class 8 maths notes on chapter Liner equation in one variable
  2. class 8 maths notes on chapter algebric expression 
  3. class 8 maths notes on chapter Mensuration 
  4. class 8 maths notes on chapter Square and square roots 
  5. class 8 maths notes on chapter statistice
  6. class 8 maths notes on chapter practical Geometry
  7. class 8 maths notes on chapter commericial maths
  8. class 8 maths notes on chapter solid shape
  9. class 8 maths notes on chapter quadrilaterals
  10. class 8 maths notes on chapter exponents
  11. class 8 maths notes on chapter factorisation 
  12. class 8 maths notes on chapter inverse proporation 
  13. class 8 maths notes on chapter cube and cube roots 

Check your marks in a chapter which you have complited in school from Physics Wallah chapter wise online test just click on the link given below

chapter wise online test for class 8 maths 

 

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