S.chand books class 8 solution maths Square and Square root

Square and Square root

 

Exercise 3 (A)

 

1.Find the square of the following numbers :

(i) 15

(ii) 48

(iii) ​\( \dfrac{6}{7} \)

(iv) ​\( \dfrac{21}{25} \)

(v) ​\( 6\dfrac{3}{8} \)

(vi) 0.9

(vii) 1.1

(viii) 0.018

2.Determine whether square of the following numbers will be even or odd.(Do not find the square)

(i) 529

(ii) 30976

(iii) 893025

(iv) 6990736

3.Just by looking at the following numbers, give reason why they are not perfect squares.

(i) 4893

(ii) 65000

(iii) 4422

(iv) 89138

(v) 150087

4.Using prime factorization method, find which of the following are perfect square numbers.

(i) 100

(ii) 284

(iii) 784

(iv) 1444

(v) 768

(vi) 4225

(vii) 3375

(viii) 15625

5.Using prime factorization method, find the square root of the following numbers.

(i) 256

(ii) 1936

(iii) 3364

(iv) 5625

(v) 7744

(vi) 12544

6.Find the square root of the following fractions.

(i) ​\( \dfrac{529}{1225} \)

(ii) \( \dfrac{1444}{3249} \)

(iii) \( 1\dfrac{396}{9604} \)

(iv) 0.01

(v) 0.1764

(vi) 0.00003136

7.Simplyfy:

(i) ​\( \sqrt{10^2-{6^2}} \)

(ii) ​\( \Bigg(-\sqrt{\dfrac{9}{16}}\Bigg)\Bigg(\sqrt{\dfrac{64}{81}}\Bigg) \)

(iii) ​\( \sqrt{\dfrac{16}{36}-\dfrac{1}{4}} \)

8.Find the square root of 1024. Hence find the value of ​\( \sqrt{10.24} + \sqrt{0.1024}+\sqrt{10240000} \)​.

9.Find the smallest number by which each of the given number s ,ust be multiplied so that the product is a perfect square. Also find the square root of this new number.

(i) 175

(ii) 325

(iii) 720

(iv) 3150

10.Find the smallest number by which each of the given numbers must be divided so that the quotient is a perfect square.Also find the square root of this quotient.

(i) 2700

(ii) 5488

(iii) 7203

(iv) 20886

11.Find the smallest number which is completely divisible by each of the numbers 10 , 16 and 24.

12.The children of class VIII of a school contributed ₹ 3025 for the Prime Minister’s National Relief Fund, contributing as much money as there are children in the class.How many children are there in the class ?

 

Exercise 3 (B)

 

1.Find the square root of each of the following numbers by division method.

(i) 3249

(ii) 6889

(iii) 15129

(iv) 75625

(v) 166464

(vi) ​9548100

(vii) ​\( \dfrac{1089}{3481} \)

(viii) ​​​\( \dfrac{7569}{14884} \)

(ix) \( 2\dfrac{337}{9216} \)

(x) ​\( 9\dfrac{4185}{5776} \)

2.Find the perimeter of a square field whose area is 13689\( m^2 \).

3.What should be subtracted from 18.246 to get a perfect square number ? What is this perfect square number ? Also, find its square root.

4.What should be added to 14841 to make the sum a perfect square ?

5.Find the least number which must be subtracted from 63520 to make it a perfect square.

6.Find:

(i) Find the least number of six digits which is a perfect square.

(ii) Find the greatest number of six digits which is a perfect square.

7.A gardener arranges his plants in rows to form a perfect square. He finds that in doing so, 25 plants are left out.If the total number of plants be 2234 , find the numbers of plants in each row.

8.There are 800 children in a school. For a PT drill they have to stand in a square formation, such that the number of rows is equal to number of columns. Find the greatest number of children needed to complete the formation.

9.Find the correct one:
The square root of 1585081 is

(a) 1259

(b) 2159

(c) 1251

(d) 1291

10.Find the value of 

\( \sqrt{240.25}+\sqrt{2.4025}+\sqrt{0.024025}+\sqrt{0.00024205} \)

(a) 1602205

(b) 16.2402

(c) 17.2205

(d) 155.2205

 

Exercise 3 (C)

 

1.Find the square root of each of the following numbers.

(i) 152.7696

(ii) 49.7025

(iii) 64.0324

(iv) 291.7264

(v) 81.108036

(vi) 0.000036

(vii) 0.00002809

(viii) 0.00033124

2.The area of a square field is 577.4409 square meters. Find the length of one side of the field.

3.Find the square root of the following numbers correct to 2 decimal places.

(i) 7

(ii) 32

(iii) 117

(iv) 512

(v) 789

(vi) 6153

(vii) 12.145956

(viii) 324.485

4.Find the square root of each of the following fraction numbers up to 3 decimal places

(i) ​\( \dfrac{2}{7} \)

(ii) ​\( \dfrac{3}{5} \)

5.Which of the following is closest to ​\( \sqrt{3} \)​ ?

(a) ​\( \dfrac{9}{5} \)

(b) 2

(c) ​\( \dfrac{173}{100} \)

(d) 1.69

6.The number of decimal places in the square root of  a number is

(a)Twice the periods in the decimal part.

(b)Half the periods in the decimal part.

(c)Equal to period in the decimal part.

(d)Half the periods in the complete number.

 

Exercise 3 (D)

 

NUMBER SQUARE SQUARE ROOT
1 1 1.000
2 4 1.414
3 9 1.732
4 16 2.000
5 25 2.236
6 36 2.449
7 49 2.646
8 64 2.828
9 81 3.000
10 100 3.162
11 121 3.317
12 144 3.464
13 169 3.606
14 196 3.742
15 225 3.873
16 256 4.000
17 289 4.123
18 324 4.243
19 361 4.359
20 400 4.472
21 441 4.583
22 484 4.690
23 529 4.796
24 576 4.899
25 625 5.000
26 676 5.099
27 729 5.196
28 784 5.292
29 841 5.385
30 900 5.477
31 961 5.568
32 1,024 5.657
33 1,089 5.745
34 1,156 5.831
35 1,225 5.916
36 1,296 6.000
37 1,369 6.083
38 1,444 6.164
39 1,521 6.245
40 1,600 6.325
41 1,681 6.403
42 1,764 6.481
43 1,849 6.557
44 1,936 6.633
45 2,025 6.708
46 2,116 6.782
47 2,209 6.856
48 2,304 6.928
49 2,401 7.000
50 2,500 7.071
51 2,601 7.141
52 2,704 7.211
53 2,809 7.280
54 2,916 7.348
55 3,025 7.416
56 3,136 7.483
57 3,249 7.550
58 3,364 7.616
59 3,481 7.681
60 3,600 7.746
61 3,721 7.810
62 3,844 7.874
63 3,969 7.937
64 4,096 8.000
65 4,225 8.062
66 4,356 8.124
67 4,489 8.185
68 4,624 8.246
69 4,761 8.307
70 4,900 8.367
71 5,041 8.426
72 5,184 8.485
73 5,329 8.544
74 5,476 8.602
75 5,625 8.660
76 5,776 8.718
77 5,929 8.775
78 6,084 8.832
79 6,241 8.888
80 6,400 8.944
81 6,561 9.000
82 6,724 9.055
83 6,889 9.110
84 7,056 9.165
85 7,225 9.220
86 7,396 9.274
87 7,569 9.327
88 7,744 9.381
89 7,921 9.434
90 8,100 9.487
91 8,281 9.539
92 8,464 9.592
93 8,649 9.644
94 8,836 9.695
95 9,025 9.747
96 9,216 9.798
97 9,409 9.849
98 9,604 9.899
99 9,801 9.950
100 10,000 10.000

 

1.Using square root table, find the square roots of the following numbers up to 3 decimal places of decimal.

(i) ​\( \sqrt{29} \)

(ii) \( \sqrt{53} \)

(iii) \( \sqrt{2100} \)

(iv) \( \sqrt{150} \)

(v) \( \sqrt{160} \)

(vi) \( \sqrt{430} \)

(vii) \( \sqrt{612} \)

(viii) \( \sqrt{325} \)

(ix) \( \sqrt{\dfrac{19}{25}} \)

(x) \( \sqrt{\dfrac{140}{121}} \)

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