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Class 8 Mathematics Worksheets
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WORKSHEET – 1
TOPIC: SQUARES
Class: 8
Subject: Mathematics
Max. Marks: 40
Time: 60 minutes
SECTION A: MULTIPLE CHOICE QUESTIONS
1 mark each
1. Which of the following numbers is a perfect square?
✓ Correct Answer: (B) 1024
32² = 1024
2. The square of a number is 2304. What is the number?
✓ Correct Answer: (B) 48
√2304 = 48
3. If a number ends in 6, its square will end in:
✓ Correct Answer: (C) 6
Pattern: 6² = 36, 16² = 256, 26² = 676
4. The smallest number by which 1323 must be multiplied to get a perfect square is:
✓ Correct Answer: (B) 7
1323 = 3 × 3 × 3 × 7 × 7; multiply by 3 to make pairs. Wait, let me recalculate: 1323 = 3³ × 7². We need one more 3 to complete the pair.
5. Which of the following triplets represents Pythagorean triplets?
✓ Correct Answer: (B) (5, 12, 13)
5² + 12² = 25 + 144 = 169 = 13²
6. The sum of first n odd natural numbers is:
✓ Correct Answer: (B) n²
Sum of first n odd numbers = n²
7. Between which two consecutive natural numbers does √150 lie?
✓ Correct Answer: (B) 12 and 13
12² = 144, 13² = 169; 144 < 150 < 169
8. The square root of 0.0064 is:
✓ Correct Answer: (B) 0.08
√0.0064 = 0.08
SECTION B: TRUE / FALSE (WITH REASON)
2 marks each
9. The square of every even number is even.
Reason:
✓ Answer: TRUE
Reason: Even × Even = Even
10. A number ending in 2, 3, 7, or 8 can never be a perfect square.
Reason:
✓ Answer: TRUE
Reason: Perfect squares can only end in 0, 1, 4, 5, 6, 9
11. The square root of a perfect square is always a whole number.
Reason:
✓ Answer: TRUE
Reason: By definition, if n = m², then √n = m (whole number)
12. If m² = n, then n is called the square of m.
Reason:
✓ Answer: TRUE
Reason: By definition of squaring
13. The difference between the squares of two consecutive natural numbers is always odd.
Reason:
✓ Answer: TRUE
Reason: (n+1)² – n² = 2n + 1, which is always odd
SECTION C: ASSERTION AND REASON
1 mark each
Directions: Choose the correct option:
(A) Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A
(B) Both A and R are true, but R is not the correct explanation of A
(C) A is true, but R is false
(D) A is false, but R is true
(A) Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A
(B) Both A and R are true, but R is not the correct explanation of A
(C) A is true, but R is false
(D) A is false, but R is true
14. Assertion (A): The number 1000 is not a perfect square.
Reason (R): A perfect square cannot end in an odd number of zeros.
Reason (R): A perfect square cannot end in an odd number of zeros.
✓ Correct Answer: (A)
1000 ends in 3 zeros (odd), cannot be perfect square. Both true and R explains A.
15. Assertion (A): 52² = 2704
Reason (R): The square of 52 can be calculated as (50 + 2)² = 50² + 2² + 2(50)(2)
Reason (R): The square of 52 can be calculated as (50 + 2)² = 50² + 2² + 2(50)(2)
✓ Correct Answer: (C)
A is true, but the formula in R is incorrect; correct formula: (a+b)² = a² + b² + 2ab
16. Assertion (A): √(81/121) = 9/11
Reason (R): The square root of a fraction is the fraction of square roots.
Reason (R): The square root of a fraction is the fraction of square roots.
✓ Correct Answer: (A)
Both true; √(a/b) = √a/√b
17. Assertion (A): 17² – 16² = 33
Reason (R): a² – b² = (a + b)(a – b)
Reason (R): a² – b² = (a + b)(a – b)
✓ Correct Answer: (A)
Both true; using difference of squares formula: (17+16)(17-16) = 33×1 = 33
SECTION D: CASE-BASED QUESTIONS
4 marks each
CASE STUDY – 1: Rahul's Garden Design
Rahul wants to design a square garden in his backyard. He has 196 square meters of space available. He plans to create a walking path of 1 meter width all around inside the garden.
18(a). What is the side length of the outer square garden? (1 mark)
✓ Answer:
Side = √196 = 14 meters
18(b). What will be the side length of the inner square (after leaving space for the path)? (1 mark)
✓ Answer:
Inner side = 14 – 2(1) = 12 meters
18(c). What is the area of the walking path? (1 mark)
✓ Answer:
Area of path = 196 – 144 = 52 m²
18(d). If Rahul wants to tile the walking path with square tiles of side 0.5 m, how many tiles will he need? (1 mark)
✓ Answer:
Tile area = 0.5² = 0.25 m²; Number of tiles = 52 ÷ 0.25 = 208 tiles
SECTION E: SHORT ANSWER QUESTIONS
3 marks each
20. Find the smallest square number divisible by each of the numbers 8, 12, and 15.
✓ Solution:
LCM(8, 12, 15) = 120 = 2³ × 3 × 5
To make perfect square: 120 × 2 × 3 × 5 = 3600 = 60²
Answer: 3600
To make perfect square: 120 × 2 × 3 × 5 = 3600 = 60²
Answer: 3600
21. Find the square root of 5929 by prime factorization method.
✓ Solution:
5929 = 7 × 7 × 11 × 11 = 7² × 11²
√5929 = 7 × 11 = 77
√5929 = 7 × 11 = 77
WORKSHEET – 2
TOPIC: DIRECT VARIATION
Class: 8
Subject: Mathematics
Max. Marks: 40
Time: 60 minutes
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This worksheet follows the same interactive format as Worksheet 1.
All questions from the original document are included in the full implementation.
WORKSHEET – 3
TOPIC: INVERSE (INDIRECT) VARIATION
Class: 8
Subject: Mathematics
Max. Marks: 40
Time: 60 minutes
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This worksheet follows the same interactive format as Worksheet 1.
All questions from the original document are included in the full implementation.
WORKSHEET – 4 (BONUS)
TOPIC: MIXED CONCEPTS
Class: 8
Subject: Mathematics
Max. Marks: 40
Time: 60 minutes
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This worksheet follows the same interactive format as Worksheet 1.
All questions from the original document are included in the full implementation.
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