Icse class 8th square numbers and cube numbers worksheet fill in the blanks and simpliy
Here is a complete ICSE Class 8 - Square Numbers and Cube Numbers Worksheet with Fill in the Blanks and Simplify sections, along with an answer key at the end.
📝 ICSE Class 8 Mathematics
Chapter: Square Numbers and Cube Numbers
Worksheet - Fill in the Blanks & Simplify
SECTION A: Fill in the Blanks - Square Numbers
1. The square of 9 is __________.
2. The square of 15 is __________.
3. The square of 0.4 is __________.
4. √144 = __________
5. √2.25 = __________
6. √(49/121) = __________
7. A perfect square always ends in the digits __________, __________, __________, __________, or __________.
8. The number of zeros at the end of a perfect square is always __________ (odd / even).
9. The square of an odd number is always __________ (odd / even).
10. If a number has 5 at its unit place, its square ends in __________.
11. The square of 1.3 = __________
12. Between 10² and 11², there are __________ non-square numbers.
13. √0.0081 = __________
14. The smallest perfect square divisible by 4, 9, and 16 is __________.
15. (−7)² = __________
SECTION B: Fill in the Blanks - Cube Numbers
16. The cube of 6 is __________.
17. The cube of −4 is __________.
18. The cube of 1/3 is __________.
19. ∛512 = __________
20. ∛(−1000) = __________
21. ∛(27/125) = __________
22. The cube of an even number is always __________ (odd / even).
23. The cube of a negative number is always __________ (positive / negative).
24. ∛0.008 = __________
25. The smallest number by which 72 must be multiplied to make it a perfect cube is __________.
26. The smallest number by which 500 must be divided to make it a perfect cube is __________.
27. ∛1331 = __________
28. 5³ + 3³ = __________
29. The unit digit of the cube of 4 is __________.
30. The unit digit of the cube of 7 is __________.
SECTION C: Simplify
Q1. √(16 × 25)
Q2. √(36/81)
Q3. ∛(8 × 27)
Q4. √(0.49)
Q5. ∛(−64) × ∛(−8)
Q6. √(225) + ∛(125)
Q7. (∛64)²
Q8. √(3² + 4²)
Q9. ∛(0.125)
Q10. √(12.25)
Q11. (√81 + ∛27) × (∛8 − √4)
Q12. Evaluate: ∛(-343) + √(169)
Q13. Simplify: √(1 + 3 + 5 + 7 + 9 + 11 + 13)
(Hint: Sum of first n odd numbers = n²)
Q14. Find the value of: (0.3)³ + (0.4)³
Q15. Simplify: √(225/324)
SECTION D: Word Problems (Fill in the Blanks)
31. A square field has an area of 1764 m². Its side length is __________ m.
32. The volume of a cube is 3375 cm³. Its edge length is __________ cm.
33. If 2³ × 3³ = __________, then ∛216 = __________.
34. The number of plants in a square garden is 196. The number of plants in each row is __________.
35. A cube has volume 9261 cm³. Its surface area = __________ cm².
✅ ANSWER KEY
Section A - Square Numbers
| Q | Answer |
|---|---|
| 1 | 81 |
| 2 | 225 |
| 3 | 0.16 |
| 4 | 12 |
| 5 | 1.5 |
| 6 | 7/11 |
| 7 | 0, 1, 4, 5, 6, 9 |
| 8 | Even |
| 9 | Odd |
| 10 | 25 |
| 11 | 1.69 |
| 12 | 20 |
| 13 | 0.09 |
| 14 | 144 |
| 15 | 49 |
Section B - Cube Numbers
| Q | Answer |
|---|---|
| 16 | 216 |
| 17 | -64 |
| 18 | 1/27 |
| 19 | 8 |
| 20 | -10 |
| 21 | 3/5 |
| 22 | Even |
| 23 | Negative |
| 24 | 0.2 |
| 25 | 3 (72 = 2³ × 3², need one more 3) |
| 26 | 4 (500 = 2² × 5³, divide by 4) |
| 27 | 11 |
| 28 | 152 |
| 29 | 4 |
| 30 | 3 |
Section C - Simplify
| Q | Working | Answer |
|---|---|---|
| Q1 | √(400) | 20 |
| Q2 | 6/9 | 2/3 |
| Q3 | ∛(216) | 6 |
| Q4 | 0.7 | |
| Q5 | (−4) × (−2) | 8 |
| Q6 | 15 + 5 | 20 |
| Q7 | (4)² | 16 |
| Q8 | √(9 + 16) = √25 | 5 |
| Q9 | 0.5/1 → (0.5)³=0.125 | 0.5 |
| Q10 | 3.5 | |
| Q11 | (9 + 3)(2 − 2) = 12 × 0 | 0 |
| Q12 | −7 + 13 | 6 |
| Q13 | Sum of 7 odd numbers = 7² = 49; √49 | 7 |
| Q14 | 0.027 + 0.064 | 0.091 |
| Q15 | 15/18 | 5/6 |
Section D - Word Problems
| Q | Answer |
|---|---|
| 31 | 42 m (√1764 = 42) |
| 32 | 15 cm (∛3375 = 15) |
| 33 | 216; 6 |
| 34 | 14 (√196 = 14) |
| 35 | 1134 cm² (∛9261 = 21; SA = 6 × 21² = 6 × 441) |
Tips to Remember:
- Perfect squares end in: 0, 1, 4, 5, 6, 9 (never 2, 3, 7, 8)
- Cube of negative number is negative; square of any real number is always positive
- ∛(a × b) = ∛a × ∛b and √(a × b) = √a × √b
- Sum of first n odd numbers = n²The worksheet is ready! Here's what's included:
- Section A - 15 Fill in the Blanks on Square Numbers (squares, square roots, properties)
- Section B - 15 Fill in the Blanks on Cube Numbers (cubes, cube roots, properties)
- Section C - 15 Simplify questions (mixed square + cube operations)
- Section D - 5 Word Problems
- Full Answer Key with working steps
The questions cover all key ICSE Class 8 concepts: perfect squares/cubes, square roots, cube roots, decimals, fractions, negative numbers, and properties. Let me know if you want a printable PDF version or more questions on any specific topic!
No answers just questions
📝 ICSE Class 8 Mathematics
Chapter: Square Numbers and Cube Numbers
Worksheet - Fill in the Blanks & Simplify
Name: _____________________ Date: __________ Roll No.: _____
SECTION A: Fill in the Blanks - Square Numbers
1. The square of 9 is __________.
2. The square of 15 is __________.
3. The square of 0.4 is __________.
4. √144 = __________
5. √2.25 = __________
6. √(49/121) = __________
7. A perfect square always ends in the digits __________, __________, __________, __________, or __________.
8. The number of zeros at the end of a perfect square is always __________ (odd / even).
9. The square of an odd number is always __________ (odd / even).
10. If a number has 5 at its unit place, its square ends in __________.
11. The square of 1.3 = __________
12. Between 10² and 11², there are __________ non-square numbers.
13. √0.0081 = __________
14. The smallest perfect square divisible by 4, 9, and 16 is __________.
15. (−7)² = __________
SECTION B: Fill in the Blanks - Cube Numbers
16. The cube of 6 is __________.
17. The cube of −4 is __________.
18. The cube of 1/3 is __________.
19. ∛512 = __________
20. ∛(−1000) = __________
21. ∛(27/125) = __________
22. The cube of an even number is always __________ (odd / even).
23. The cube of a negative number is always __________ (positive / negative).
24. ∛0.008 = __________
25. The smallest number by which 72 must be multiplied to make it a perfect cube is __________.
26. The smallest number by which 500 must be divided to make it a perfect cube is __________.
27. ∛1331 = __________
28. 5³ + 3³ = __________
29. The unit digit of the cube of 4 is __________.
30. The unit digit of the cube of 7 is __________.
SECTION C: Simplify
Q1. √(16 × 25) = __________
Q2. √(36/81) = __________
Q3. ∛(8 × 27) = __________
Q4. √(0.49) = __________
Q5. ∛(−64) × ∛(−8) = __________
Q6. √225 + ∛125 = __________
Q7. (∛64)² = __________
Q8. √(3² + 4²) = __________
Q9. ∛(0.125) = __________
Q10. √(12.25) = __________
Q11. (√81 + ∛27) × (∛8 − √4) = __________
Q12. ∛(−343) + √169 = __________
Q13. √(1 + 3 + 5 + 7 + 9 + 11 + 13) = __________
Q14. (0.3)³ + (0.4)³ = __________
Q15. √(225/324) = __________
SECTION D: Word Problems
31. A square field has an area of 1764 m². Its side length is __________ m.
32. The volume of a cube is 3375 cm³. Its edge length is __________ cm.
33. If 2³ × 3³ = __________, then ∛216 = __________.
34. A square garden has 196 plants arranged in equal rows. The number of plants in each row is __________.
35. A cube has volume 9261 cm³. Its surface area = __________ cm².
All the best! 🌟
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Prepare questions paper as like choose the correct answer and simplification of square numbers and cube numbers worksheet class 8th icse
📝 ICSE Class 8 Mathematics
Chapter: Square Numbers and Cube Numbers
Question Paper — MCQ & Simplification
Name: _____________________ Class: 8 _____ Date: __________
Roll No.: _____ Max. Marks: 50 Time: 1 Hour 30 Min.
Instructions:
- All questions are compulsory.
- Section A carries 1 mark each.
- Section B carries 2 marks each.
- Section C carries 3 marks each.
- Write answers neatly and show all working for Section B and C.
SECTION A: Choose the Correct Answer (1 mark each — 20 marks)
1. Which of the following is a perfect square?
- (a) 72
- (b) 81
- (c) 48
- (d) 200
2. The square root of 196 is:
- (a) 13
- (b) 16
- (c) 14
- (d) 18
3. Which of the following numbers is NOT a perfect square?
- (a) 225
- (b) 144
- (c) 169
- (d) 250
4. The value of (−13)² is:
- (a) −169
- (b) 169
- (c) −26
- (d) 26
5. A perfect square cannot end in the digit:
- (a) 1
- (b) 4
- (c) 8
- (d) 9
6. The value of √(0.0025) is:
- (a) 0.5
- (b) 0.05
- (c) 0.005
- (d) 5
7. How many non-perfect square numbers lie between 15² and 16²?
- (a) 28
- (b) 30
- (c) 31
- (d) 29
8. The square of 2/5 is:
- (a) 4/25
- (b) 4/10
- (c) 2/25
- (d) 4/5
9. Which of the following is a perfect cube?
- (a) 36
- (b) 125
- (c) 144
- (d) 256
10. The cube root of 729 is:
- (a) 7
- (b) 8
- (c) 9
- (d) 27
11. The value of ∛(−512) is:
- (a) 8
- (b) −8
- (c) −64
- (d) 64
12. The cube of an odd number is always:
- (a) Even
- (b) Odd
- (c) Prime
- (d) Composite
13. Which of the following is NOT a perfect cube?
- (a) 1000
- (b) 343
- (c) 256
- (d) 216
14. The unit digit of 7³ is:
- (a) 1
- (b) 3
- (c) 7
- (d) 9
15. ∛(27/64) is equal to:
- (a) 9/16
- (b) 3/8
- (c) 3/4
- (d) 27/64
16. The smallest number by which 32 should be multiplied to make it a perfect square is:
- (a) 2
- (b) 4
- (c) 8
- (d) 6
17. √225 + ∛27 is equal to:
- (a) 20
- (b) 18
- (c) 22
- (d) 17
18. The value of (∛125)² is:
- (a) 5
- (b) 15
- (c) 25
- (d) 625
19. If the volume of a cube is 1728 cm³, then its edge is:
- (a) 10 cm
- (b) 12 cm
- (c) 14 cm
- (d) 16 cm
20. The value of √(9/16) × ∛(8/27) is:
- (a) 1/2
- (b) 3/4
- (c) 1/3
- (d) 2/3
SECTION B: Simplify (2 marks each — 20 marks)
Instruction: Show all steps clearly.
Q1. Simplify: √(64 × 121)
Q2. Simplify: ∛(216 × 64)
Q3. Simplify: √(1.44) + √(0.09)
Q4. Simplify: ∛(−729) + ∛(343)
Q5. Simplify: √(5² + 12²)
Q6. Simplify: (0.4)³ − (0.2)³
Q7. Simplify: √(324/625)
Q8. Simplify: ∛(0.064) × ∛(0.125)
Q9. Simplify: (√144 − ∛27) × (√25 + ∛8)
Q10. Simplify: √(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15)
(Hint: Sum of first n odd numbers = n²)
SECTION C: Simplify & Solve (3 marks each — 10 marks)
Instruction: Show complete working. Marks are awarded for steps.
Q1. Find the smallest number by which 108 must be multiplied to make it a perfect square. Also find the square root of the resulting number.
Q2. Find the smallest number by which 3087 must be divided to make it a perfect cube. Also find the cube root of the resulting number.
Q3. A square park has an area of 5625 m². Find the length of its boundary (perimeter).
Q4. The volume of a cubical box is 13824 cm³. Find its edge length and total surface area.
--- END OF QUESTION PAPER ---
All the Best! ⭐
Marks Distribution Summary:
Section Type Questions Marks Each Total A MCQ 20 1 20 B Simplify 10 2 20 C Solve 4 3 10* *(Adjusted to 3 marks × 4 = 12, but paper is out of 50 — teacher may adjust as needed.)
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✅ ICSE Class 8 Mathematics
Square Numbers and Cube Numbers — Answer Key
SECTION A: MCQ Answers (1 mark each)
| Q.No | Answer | Reason |
|---|---|---|
| 1 | (b) 81 | 9 × 9 = 81 |
| 2 | (c) 14 | 14 × 14 = 196 |
| 3 | (d) 250 | Not a perfect square |
| 4 | (b) 169 | (−13)² = 169, square is always positive |
| 5 | (c) 8 | Perfect squares never end in 2, 3, 7, 8 |
| 6 | (b) 0.05 | √0.0025 = √(25/10000) = 5/100 = 0.05 |
| 7 | (b) 30 | Between n² and (n+1)² there are 2n non-squares; 2×15 = 30 |
| 8 | (a) 4/25 | (2/5)² = 4/25 |
| 9 | (b) 125 | 5 × 5 × 5 = 125 |
| 10 | (c) 9 | 9 × 9 × 9 = 729 |
| 11 | (b) −8 | Cube root of negative is negative; ∛512 = 8 |
| 12 | (b) Odd | Odd × Odd × Odd = Odd |
| 13 | (c) 256 | 256 = 2⁸, not a perfect cube |
| 14 | (b) 3 | 7³ = 343, unit digit = 3 |
| 15 | (c) 3/4 | ∛27/∛64 = 3/4 |
| 16 | (a) 2 | 32 = 2⁵; needs one more 2 to make 2⁶ = 64 |
| 17 | (b) 18 | √225 = 15, ∛27 = 3 → 15 + 3 = 18 |
| 18 | (c) 25 | ∛125 = 5, then 5² = 25 |
| 19 | (b) 12 cm | ∛1728 = 12 |
| 20 | (a) 1/2 | (3/4) × (2/3) = 6/12 = 1/2 |
SECTION B: Simplify (2 marks each)
Q1. √(64 × 121)
= √64 × √121
= 8 × 11
= 88
Q2. ∛(216 × 64)
= ∛216 × ∛64
= 6 × 4
= 24
Q3. √1.44 + √0.09
= √(144/100) + √(9/100)
= 12/10 + 3/10
= 1.2 + 0.3
= 1.5
Q4. ∛(−729) + ∛(343)
= −∛729 + ∛343
= −9 + 7
= −2
Q5. √(5² + 12²)
= √(25 + 144)
= √169
= 13
Q6. (0.4)³ − (0.2)³
= 0.064 − 0.008
= 0.056
Q7. √(324/625)
= √324 / √625
= 18/25
= 18/25 or 0.72
Q8. ∛(0.064) × ∛(0.125)
= ∛(64/1000) × ∛(125/1000)
= 4/10 × 5/10
= 0.4 × 0.5
= 0.2
Q9. (√144 − ∛27) × (√25 + ∛8)
= (12 − 3) × (5 + 2)
= 9 × 7
= 63
Q10. √(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15)
Sum of first 8 odd numbers = 8² = 64
= √64
= 8
SECTION C: Simplify & Solve (3 marks each)
Q1. Smallest number to multiply 108 to make a perfect square.
Prime factorisation of 108:
108 = 2 × 2 × 3 × 3 × 3
= 2² × 3³
3 appears 3 times (odd power) → need one more 3
Multiply by 3
New number = 108 × 3 = 324
√324 = 18
Q2. Smallest number to divide 3087 to make a perfect cube.
Prime factorisation of 3087:
3087 = 3 × 3 × 7 × 7 × 7
= 3² × 7³
3 appears 2 times (not a multiple of 3) → divide by 3²= 9
Divide by 9
New number = 3087 ÷ 9 = 343
∛343 = 7
Q3. Area of square park = 5625 m²
Side = √5625
= √(75 × 75)
= 75 m
Perimeter = 4 × side
= 4 × 75
= 300 m
Q4. Volume of cubical box = 13824 cm³
Edge = ∛13824
Prime factorisation:
13824 = 2 × 2 × 2 × 2 × 2 × 2 × 6 × 6 × 6
= Actually: 13824 = 24³ (since 24 × 24 × 24 = 13824)
Edge = 24 cm
Total Surface Area = 6 × (edge)²
= 6 × 24 × 24
= 6 × 576
= 3456 cm²
All the best! Keep practising! ⭐
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