Exercise 3.9 of RD Sharma Solutions for the Class 8 Maths Chapter 3, Squares and Square Roots. Students can refer and download from the links provided below. Our expert team at BYJUâ€™S have solved the RD SharmaÂ Solutions for Class 8Â that help students practice the problems without any obstacles. Exercise 3.9 of Class 8 is about finding the approximate values of square roots by using square root tables. Practice RD Sharma Solutions for Class 8 for better understanding of the concepts, which help students obtain high marks in their examination.
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EXERCISE 3.9 PAGE NO: 3.61
Square Root Table |
|||||||||
Number |
Square Root(âˆš) |
Number |
Square Root(âˆš) |
Number |
Square Root(âˆš) |
Number |
Square Root(âˆš) |
Number |
Square Root(âˆš) |
1 |
1 |
21 |
4.583 |
41 |
6.403 |
61 |
7.81 |
81 |
9 |
2 |
1.414 |
22 |
4.69 |
42 |
6.481 |
62 |
7.874 |
82 |
9.055 |
3 |
1.732 |
23 |
4.796 |
43 |
6.557 |
63 |
7.937 |
83 |
9.11 |
4 |
2 |
24 |
4.899 |
44 |
6.633 |
64 |
8 |
84 |
9.165 |
5 |
2.236 |
25 |
5 |
45 |
6.708 |
65 |
8.062 |
85 |
9.22 |
6 |
2.449 |
26 |
5.099 |
46 |
6.782 |
66 |
8.124 |
86 |
9.274 |
7 |
2.646 |
27 |
5.196 |
47 |
6.856 |
67 |
8.185 |
87 |
9.327 |
8 |
2.828 |
28 |
5.292 |
48 |
6.928 |
68 |
8.246 |
88 |
9.381 |
9 |
3 |
29 |
5.385 |
49 |
7 |
69 |
8.307 |
89 |
9.434 |
10 |
3.162 |
30 |
5.477 |
50 |
7.071 |
70 |
8.367 |
90 |
9.487 |
11 |
3.317 |
31 |
5.568 |
51 |
7.141 |
71 |
8.426 |
91 |
9.539 |
12 |
3.464 |
32 |
5.657 |
52 |
7.211 |
72 |
8.485 |
92 |
9.592 |
13 |
3.606 |
33 |
5.745 |
53 |
7.28 |
73 |
8.544 |
93 |
9.644 |
14 |
3.742 |
34 |
5.831 |
54 |
7.348 |
74 |
8.602 |
94 |
9.695 |
15 |
3.873 |
35 |
5.916 |
55 |
7.416 |
75 |
8.66 |
95 |
9.747 |
16 |
4 |
36 |
6 |
56 |
7.483 |
76 |
8.718 |
96 |
9.798 |
17 |
4.123 |
37 |
6.083 |
57 |
7.55 |
77 |
8.775 |
97 |
9.849 |
18 |
4.243 |
28 |
6.164 |
58 |
7.616 |
78 |
8.832 |
98 |
9.899 |
19 |
4.359 |
29 |
6.245 |
59 |
7.681 |
79 |
8.888 |
99 |
9.95 |
20 |
4.472 |
40 |
6.325 |
60 |
7.746 |
80 |
8.944 |
100 |
10 |
Using square root table, find the square roots of the following:
1. 7
Solution:
From square root table we know,
Square root of 7 is:
âˆš7 = 2.645
âˆ´ The square root of 7 is 2.645
2. 15
Solution:
We know that,
15 = 3 x 5
So, âˆš15 = âˆš3 x âˆš5
From square root table we know,
Square root of 3 and 5 are:
âˆš3 = 1.732 and âˆš5 = 2.236
â‡’ âˆš15 = 1.732 x 2.236 = 3.873
âˆ´ The square root of 15 is 3.873
3. 74
Solution:
We know that,
74 = 2 x 37
So, âˆš74 = âˆš2 x âˆš37
From square root table we know,
Square root of 2 and 37 are:
âˆš2 = 1.414 and âˆš37 = 6.083
â‡’ âˆš74 = 1.414 x 6.083 = 8.602
âˆ´ The square root of 74 is 8.602
4. 82
Solution:
We know that,
82 = 2 x 41
So, âˆš82 = âˆš2 x âˆš41
From square root table we know,
Square root of 2 and 41 are:
âˆš2 = 1.414 and âˆš41 = 6.403
â‡’ âˆš82 = 1.414 x 6.403 = 9.055
âˆ´ The square root of 82 is 9.055
5. 198
Solution:
We know that,
198 = 2 x 9 x 11
So, âˆš198 = âˆš2 x âˆš9 x âˆš11
From square root table we know,
Square root of 2, 9 and 11 are:
âˆš2 = 1.414, âˆš9 = 3 and âˆš11 = 3.317
â‡’ âˆš198 = 1.414 x 3 x 3.317 = 14.071
âˆ´ The square root of 198 is 14.071
6. 540
Solution:
We know that,
540 = 6 x 9 x 10
So, âˆš540 = âˆš6 x âˆš9 x âˆš10
From square root table we know,
Square root of 6, 9 and 10 are:
âˆš6 = 2.449, âˆš9 = 3 and âˆš10 = 3.162
â‡’ âˆš540 = 2.449 x 3 x 3.162 = 23.24
âˆ´ The square root of 540 is 23.24
7. 8700
Solution:
We know that,
8700 = 87 x 100
So, âˆš8700 = âˆš87 x âˆš100
From square root table we know,
Square root of 87 and 100 are:
âˆš8700 = 9.327 and âˆš100 = 10
â‡’ âˆš8700 = 9.327 x 10 = 93.27
âˆ´ The square root of 8700 is 93.27
8. 3509
Solution:
We know that,
3509 = 121 x 29
So, âˆš3509 = âˆš121 x âˆš29
From square root table we know,
Square root of 121 and 29 are:
âˆš121 = 11 and âˆš29 = 5.385
â‡’ âˆš3509 = 11 x 10 = 5.385
âˆ´ The square root of 3509 is 59.235
9. 6929
Solution:
We know that,
6929 = 169 x 41
So, âˆš6929 = âˆš169 x âˆš41
From square root table we know,
Square root of 169 and 41 are:
âˆš169 = 13 and âˆš41 = 6.403
â‡’ âˆš6929 = 13 x 6.403 = 83.239
âˆ´ The square root of 6929 is 83.239
10. 25725
Solution:
We know that,
25725 = 3 x 7 x 25 x 49
So, âˆš25725 = âˆš3 x âˆš7 x âˆš25 x âˆš49
From square root table we know,
Square root of 3, 7, 25 and 49 are:
âˆš3 = 1.732, âˆš7 = 2.646, âˆš25 = 5 and âˆš49 = 7
â‡’ âˆš25725 = 1.732 x 2.646 x 5 x 7 = 160.41
âˆ´ The square root of 25725 is 160.41
11. 1312.
Solution:
We know that,
1312 = 2 x 16 x 41
So, âˆš1312 = âˆš2 x âˆš16 x âˆš41
From square root table we know,
Square root of 2, 16 and 41 are:
âˆš2 = 1.414, âˆš16 = 4 and âˆš41 = 6.403
â‡’ âˆš1312 = 1.414 x 4 x 6.403 = 36.22
âˆ´ The square root of 1312 is 36.22
12. 4192
Solution:
We know that,
4192 = 2 x 16 x 131
So, âˆš4192 = âˆš2 x âˆš16 x âˆš131
From square root table we know,
Square root of 2 and16 are:
âˆš2 = 1.414 and âˆš16 = 4
The square root of 131 is not listed in the table
Thus, letâ€™s apply long division to find it
So, square root of 131 is 11.445
Now,
â‡’ âˆš4192 = 1.414 x 4 x 11.445 = 64.75
âˆ´ The square root of 4192 is 64.75
13. 4955
Solution:
We know that,
4955 = 5 x 991
So, âˆš4955 = âˆš5 x âˆš991
From square root table we know,
Square root of 5 is:
âˆš5 = 2.236
The square root of 991 is not listed in the table
Thus, letâ€™s apply long division to find it
So, square root of 991 is 31.480
Now,
â‡’ âˆš4955 = 2.236 x 31.480 = 70.39
âˆ´ The square root of 4955 is 70.39
14. 99/144
Solution:
We know that,
99/144 = (9 x 11) / (12 x 12)
So, âˆš(99/144) = âˆš[(9 x 11) x (12 x 12)]
= 3/12 x âˆš11
From square root table we know,
Square root of 11 is:
âˆš11 = 3.317
â‡’ âˆš(99/144) = 3/12 x 3.317 = 3.317/4 = 0.829
âˆ´ The square root of 99/144 is 0.829
15. 57/169
Solution:
We know that,
57/169 = (3 x 19) / (13 x 13)
So, âˆš(57/169) = âˆš[(3 x 19) x (13 x 13)]
= âˆš3 x âˆš19 x 1/13
From square root table we know,
Square root of 3 and 19 is:
âˆš3 = 1.732 and âˆš19 = 4.359
â‡’ âˆš(57/169) = 1.732 x 4.359 x 1/13 = 0.581
âˆ´ The square root of 57/169 is 0.581
16. 101/169
Solution:
We know that,
101/169 = 101 / (13 x 13)
So, âˆš(101/169) = âˆš[101 / (13 x 13)]
= âˆš101/13
From square root table we donâ€™t have the square root of 101
Thus, we have to manipulate the number such that we get the square root of a number less than 100
âˆš101 = âˆš(1.01 x 100)
= âˆš1.01 x 10
Now, we have to find the square of 1.01
We know that,
âˆš1 = 1 and âˆš2 = 1.414 (From the square root table)
Their difference = 1.414 â€“ 1 = 0.414
Hence, for a difference of 1 (2 – 1), the difference in the value of the square root is 0.414
So,
For the difference of 0.01, the difference in the value of the square roots will be
0.01 x 1.414 = 0.00414
âˆ´âˆš1.01 = 1 + 0.00414 = 1.00414
Then, âˆš101 = 1.00414 x 10 = 10.0414
â‡’ âˆš(101/169) = âˆš101/13 = 10.0414/13
âˆ´ The square root of 101/169 is 0.773
17. 13.21
Solution:
We need to find âˆš13.21
From square root table we know,
Square root of 13 and 14 are:
âˆš13 = 3.606 and âˆš14 = 3.742
Their difference = 3.742 â€“ 3.606 = 0.136
Hence, for a difference of 1 (14 – 13), the difference in the value of the square root is 0.136
So,
For the difference of 0.21, the difference in the value of the square roots will be
0.136 x 0.21 = 0.0286
â‡’ âˆš13.21 = 3.606 + 0.0286 = 3.635
âˆ´ The square root of 13.21 is 3.635
18. 21.97
Solution:
We need to find âˆš21.97
From square root table we know,
Square root of 21 and 22 are:
âˆš21 = 4.583 and âˆš22 = 4.690
Their difference = 4.690 â€“ 4.583 = 0.107
Hence, for a difference of 1 (23 – 22), the difference in the value of the square root is 0.107
So,
For the difference of 0.97, the difference in the value of the square roots will be
0.107 x 0.97 = 0.104
â‡’ âˆš21.97 = 4.583 + 0.104 = 4.687
âˆ´ The square root of 21.97 is 4.687
19. 110
Solution:
We know that,
110 = 11 x 10
So, âˆš110 = âˆš11 x âˆš10
From square root table we know,
Square root of 11 and 10 are:
âˆš11 = 3.317 and âˆš10 = 3.162
â‡’ âˆš110 = 3.317 x 3.162 = 10.488
âˆ´ The square root of 110 is 10.488
20. 1110
Solution:
We know that,
1110 = 37 x 30
So, âˆš1110 = âˆš37 x âˆš30
From square root table we know,
Square root of 37 and 30 are:
âˆš37 = 6.083 and âˆš30 = 5.477
â‡’ âˆš1110 = 6.083 x 5.477 = 33.317
âˆ´ The square root of 1110 is 33.317
21. 11.11
Solution:
We need to find âˆš11.11
From square root table we know,
Square root of 11 and 12 are:
âˆš11 = 3.317 and âˆš12 = 3.464
Their difference = 3.464 â€“ 3.317 = 0.147
Hence, for a difference of 1 (12 – 11), the difference in the value of the square root is 0.147
So,
For the difference of 0.11, the difference in the value of the square roots will be
0.11 x 0.147 = 0.01617
â‡’ âˆš11.11 = 3.317 + 0.0162 = 3.333
âˆ´ The square root of 11.11 is 3.333
22. The area of a square field is 325m^{2}. Find the approximate length of one side of the field.
Solution:
We know that the given area of the field = 325 m^{2}
To find the approximate length of the side of the field we will have to calculate the square root of 325
âˆš325 = âˆš25 x âˆš13
From the square root table, we know
âˆš25 = 5 and âˆš13 = 3.606
â‡’ âˆš325 = 5 x 3.606 = 18.030
âˆ´ The approximate length of one side of the field is 18.030 m
23. Find the length of a side of a square, whose area is equal to the area of a rectangle with sides 240 m and 70 m.
Solution:
We know that from the question,
Area of square = Area of rectangle
Side^{2} = 240 Ã— 70
Side = âˆš(240 Ã— 70)
= âˆš(10 Ã— 10 Ã— 2 Ã— 2 Ã— 2 Ã— 3 Ã— 7)
= 20âˆš42
Now, from the square root table, we know âˆš42 = 6.481
= 20 Ã— 6.48
= 129.60 m
âˆ´ The length of side of the square is 129.60 m
RD Sharma Solutions for Class 8 Maths Exercise 3.9 Chapter 3 – Squares and Square Roots
Exercise 3.9 of RD Sharma Solutions for Chapter 3 Squares and Square Roots, this exercise mainly deals with the concepts related to finding the approximate values of square roots by using square root tables. The students can solve problems of RD Sharma textbook for Class 8 using the solutions as reference material. This mainly improves confidence among students in solving tricky and lengthy problems easily. The PDF is easily accessible by the students which help in speeding up their exam preparation.