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Chapter-1 A Square and A Cube — Online MCQ Test

MATHS (KANITHA PRAKASH) · CLASS 8th · Karnataka State Board

Practice Chapter-1 A Square and A Cube with a free chapter-wise online MCQ test for Karnataka State Board CLASS 8th MATHS (KANITHA PRAKASH). This chapter covers: perfect square - square root - radicals - perfect cube - cube root - prime factorisation - long division method - estimating roots. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter-1 A Square and A Cube — Important Questions & Answers (FAQ)

Frequently asked questions from Karnataka State Board CLASS 8th MATHS (KANITHA PRAKASH) — Chapter-1 A Square and A Cube, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is a perfect square?
  • A. A number that is the product of two equal integers ✓
  • B. A number divisible by 2
  • C. A number greater than 10
  • D. A number with all digits the same
Answer: A. A number that is the product of two equal integers
A perfect square is obtained by multiplying an integer by itself, such as 4 = 2×2, 9 = 3×3.
Which of the following is a perfect square?
  • A. 35
  • B. 49 ✓
  • C. 50
  • D. 48
Answer: B. 49
49 = 7 × 7, making it a perfect square. The others are not products of equal integers.
The square root of 144 is ____.
  • A. 10
  • B. 11
  • C. 12 ✓
  • D. 13
Answer: C. 12
√144 = 12 because 12 × 12 = 144.
What is the symbol used to denote square root?
  • A. √ ✓
  • B. ∛
  • C. ^
  • D. ÷
Answer: A. √
The radical symbol √ is used to denote square root. ∛ denotes cube root.
Find √225.
  • A. 13
  • B. 14
  • C. 15 ✓
  • D. 16
Answer: C. 15
√225 = 15 because 15 × 15 = 225.
What is the prime factorisation of 36?
  • A. 2 × 3 × 6
  • B. 2² × 3² ✓
  • C. 2 × 18
  • D. 3 × 12
Answer: B. 2² × 3²
36 = 2 × 2 × 3 × 3 = 2² × 3². This expresses 36 as a product of only prime numbers.
If a number's prime factorisation is 2² × 5², what is its square root?
  • A. 10 ✓
  • B. 20
  • C. 100
  • D. 5
Answer: A. 10
2² × 5² = (2 × 5)² = 10². Therefore, √(2² × 5²) = 2 × 5 = 10.
Estimate √77 and choose the closest value.
  • A. 8.5
  • B. 8.7
  • C. 8.9 ✓
  • D. 9.2
Answer: C. 8.9
Since 8.9² ≈ 79.21 and 8.8² ≈ 77.44, √77 is closest to 8.8-8.9. The option 8.9 is nearest.
If √(x + 5) = 7, then x = ____.
  • A. 44 ✓
  • B. 49
  • C. 54
  • D. 64
Answer: A. 44
√(x + 5) = 7 means x + 5 = 49, so x = 44. Squaring both sides gives us the value of x.
The prime factorisation of a perfect square is 2⁴ × 3² × 5². What is its square root?
  • A. 60 ✓
  • B. 120
  • C. 180
  • D. 360
Answer: A. 60
2⁴ × 3² × 5² = (2² × 3 × 5)² = (4 × 3 × 5)² = 60². Therefore, √(2⁴ × 3² × 5²) = 2² × 3 × 5 = 60.

More MATHS (KANITHA PRAKASH) Chapters

Chapter-2 Power Play Chapter-3 A Story of Numbers Chapter-4 Quadrilaterals Chapter-5 Number Play Chapter-6 We Distribute Chapter-7 Proportional Reasoning

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