# 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) $$\sqrt{\dfrac{140}{121}}$$