Class-8 Ganita prakash Worksheet Maths ch-1

Class-VIII Ganita prakash Worksheet   (2025-2026)                    Subject: Maths

                                                     

1. If a number ends in 0, 1, 4, 5, 6 or 9, is it always a square?

2. Write 5 numbers such that you can determine by looking at their units digit that they are not squares.

3. Which of the following numbers have the digit 6 in the unit's place?
   (i) 38² (ii) 34² (iii) 46² (iv) 56² (v) 74² (vi) 82²

4. If a number contains 3 zeros at the end, how many zeros will its square have at the end?

5. What can you say about the parity of a number and its square?

6. Using the sum of successive odd numbers pattern, find 36², given that 35² = 1225.

7. What is the nth odd number?
   a) 2n b) 2n-1 c) n +1 d) n+2

8. The 36th odd number is ____
   a) 71 b)81 c)101 d)91

9. Find how many numbers lie between two consecutive (m,m+1) perfect squares?
   a)2m b) 3m c) 4m d) m 

10. How many square numbers are there between 1 and 100? 

11. How many are between 101 and 200?

12.  What is the largest square less than 1000?

13.  Extend the pattern shown and draw the next term. 

14.  The area of a square is 49 sq. cm. What is the length of its side?

15. if y= x² then x is the square root of ______

16. What is the square root of 64?

17.   n2  = __________ a ) ± n b) 0 c) 2 d) -n,-m

18. find out if 576 or 327 is a perfect square? If it is a perfect square, find its square root? If not write the reason.

19. Is 324 a perfect square?

20. Is 156 a perfect square? 

21. Find whether 1156 and 2800 are perfect squares using prime factorisation

22. 1. Which of the following numbers are not perfect squares? (i) 2032 (ii) 2048 (iii) 1027 (iv) 1089 

23. 2. Which one among 642, 1082, 2922, 362 has last digit 4?

24.  3. Given 125² = 15625, what is the value of 126²? (i) 15625 + 126 (ii) 15625 + 26² (iv) 15625 + 251 (iii) 15625 + 253 (v) 15625 + 51² 

25. 4. Find the length of the side of a square whose area is 441 m². 

26. 5. Find the smallest square number that is divisible by each of the following numbers: 4, 9, and 10. 

27. 6. Find the smallest number by which 9408 must be multiplied so that the product is a perfect square. Find the square root of the product. 

28. 7. How many numbers lie between the squares of the following numbers? (i) 16 and 17 (ii) 99 and 100

29. 8. In the following pattern, fill in the missing numbers 

1² + 2² + 2² = 3²

 2² + 3² + 6² = 7² 

3² + 4² + 12² = 13² 

4² + 5² + 20² = (___)²

 9² + 10² + (___)² = (___)² 

30. 9. How many tiny squares are there in the following picture? Write the prime factorisation of the number of tiny squares.

31. How many cubes of side 1 cm will make a cube of side 3 cm?

32.  How many cubes of side 1 cm make a cube of side 2 cm?

33. Is 9 a cube? 

34.  estimate the number of unit cubes in a cube with an edge length of 4 units?

35. We know that 0, 1, 4, 5, 6, 9 are the only last digits possible for squares. What are the possible last digits of cubes?

36. Similar to squares, can you find the number of cubes with 1 digit, 2 digits, and 3 digits? What do you observe?

37. Can a cube end with exactly two zeroes (00)? Explain.

38.  The next two taxicab numbers after 1729 are 4104 and 13832. Find the two ways in which each of these can be expressed as the sum of two positive cubes.

39.  1 = 1 = 1³ 

3 + 5 = 8 = 2³

 7 + 9 + 11 = 27 = 3³

13 + 15 + 17 + 19 = 64 = 4³

21 + 23 + 25 + 27 + 29 = 125 = 5³ 

31 + 33 + 35 + 37 + 39 + 41 = 216 = 6³.

…………………. 

91 + 93 + 95 + 97 + 99 + 101 + 103 + 105 + 107 + 109.  what is this sum without doing the calculation?

40. check if 3375 is a perfect cube.

41. Is 500 a perfect cube?

42. Find the cube roots of these numbers: (i) 364  (ii)  3512  (iii)  3729  

43. Compute successive differences over levels for perfect cubes until all the differences at a level are the same. What do you notice? Perfect Cubes 1 8 27 64 125 216 ..

44. Find the cube roots of 27000 and 10648. 

45. 2. What number will you multiply by 1323 to make it a cube number? 

46. 3. State true or false. Explain your reasoning. 

(i) The cube of any odd number is even. 

(ii) There is no perfect cube that ends with 8. 

(iii) The cube of a 2-digit number may be a 3-digit number. 

(iv) The cube of a 2-digit number may have seven or more digits. 

(v) Cube numbers have an odd number of factors.

47. 4. You are told that 1331 is a perfect cube. Can you guess without factorisation what its cube root is? Similarly, guess the cube roots of 4913, 12167, and 32768

48. Square root is the inverse operation of _____________

49. A number obtained by multiplying a number by itself three times is called a ________.

50.  A number is a perfect cube if its prime factors can be split into _______ identical groups 

51. Which of the following is the greatest? Explain your reasoning.

 (i) 67³ – 66³ (ii) 43³ – 42³ (iii) 67² – 66² (iv) 43² – 42²