Class 8 Mathematics Worksheet

Squares and Square Roots

Name: ____________________  Class: ________  Date: __________

Key Formula

$$\text{Square of a number} = n^2,\qquad \text{Square Root of a perfect square} = \sqrt{n^2}=n$$Square of a number=n2,Square Root of a perfect square=n2​=n

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Section A: Multiple Choice Questions (10 × 1 = 10 Marks)

1. The square of 15 is:
   a) 215 b) 225 c) 235 d) 245
2. √144 = _______
   a) 10 b) 11 c) 12 d) 13
3. Which of the following is a perfect square?
   a) 72 b) 81 c) 95 d) 108
4. The square root of 225 is:
   a) 12 b) 13 c) 15 d) 25
5. Which number ends with 25 when squared?
   a) 15 b) 14 c) 16 d) 18
6. √625 = _______
7. Which of the following is not a perfect square?
   a) 196 b) 225 c) 250 d) 289
8. Square of 24 is:
   a) 484 b) 576 c) 625 d) 676
9. √400 = _______
10. The square root of 1 is:
    a) 0 b) 1 c) 2 d) 10

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Section B: Find the Squares (10 × 2 = 20 Marks)

11. 12²
12. 14²
13. 18²
14. 21²
15. 25²
16. 28²
17. 32²
18. 35²
19. 42²
20. 50²

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Section C: Find the Square Roots (10 × 2 = 20 Marks)

21. √49
22. √64
23. √81
24. √100
25. √121
26. √169
27. √256
28. √324
29. √441
30. √900

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Section D: Fill in the Blanks (10 × 2 = 20 Marks)

31. 17² = _______
32. √361 = _______
33. The square of 40 is _______.
34. √784 = _______
35. 19² = _______
36. √529 = _______
37. 45² = _______
38. √676 = _______
39. 27² = _______
40. √961 = _______

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Section E: True or False (10 × 1 = 10 Marks)

41. 144 is a perfect square.
42. √225 = 16.
43. 36² = 1296.
44. √625 = 25.
45. 500 is a perfect square.
46. The square of an even number is even.
47. The square of an odd number is odd.
48. √1 = 1.
49. 900 is a perfect square.
50. √729 = 27.

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Section F: Word Problems (10 × 2 = 20 Marks)

51. A square park has a side of 18 m. Find its area.
52. A square tile has a side of 25 cm. Find its area.
53. The area of a square field is 400 m². Find its side.
54. A square garden has an area of 625 m². Find its side length.
55. A square floor has a side of 12 m. Find its area.
56. Find the smallest perfect square divisible by 9.
57. Find the square of 99.
58. Find the square root of 1600.
59. A square photo frame has an area of 324 cm². Find its side.
60. Find the difference between the squares of 30 and 20.

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Answer Key

1. b) 225
2. 12
3. 81
4. 15
5. 15
6. 25
7. 250
8. 576
9. 20
10. 1
11. 144
12. 196
13. 324
14. 441
15. 625
16. 784
17. 1024
18. 1225
19. 1764
20. 2500
21. 7
22. 8
23. 9
24. 10
25. 11
26. 13
27. 16
28. 18
29. 21
30. 30
31. 289
32. 19
33. 1600
34. 28
35. 361
36. 23
37. 2025
38. 26
39. 729
40. 31
41. True
42. False
43. True
44. True
45. False
46. True
47. True
48. True
49. True
50. True
51. 324 m²
52. 625 cm²
53. 20 m
54. 25 m
55. 144 m²
56. 9
57. 9801
58. 40
59. 18 cm
60. 500