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:
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 

x 

x 

x 

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
 class 8 maths notes on chapter Liner equation in one variable
 class 8 maths notes on chapter algebric expression
 class 8 maths notes on chapter Mensuration
 class 8 maths notes on chapter Square and square roots
 class 8 maths notes on chapter statistice
 class 8 maths notes on chapter practical Geometry
 class 8 maths notes on chapter commericial maths
 class 8 maths notes on chapter solid shape
 class 8 maths notes on chapter quadrilaterals
 class 8 maths notes on chapter exponents
 class 8 maths notes on chapter factorisation
 class 8 maths notes on chapter inverse proporation
 class 8 maths notes on chapter cube and cube roots
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