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.
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.
Chapter-1 A Square and A Cube — Important Questions & Answers
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.
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.
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.
√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.
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.
√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.
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.
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.
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.
√(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.
2⁴ × 3² × 5² = (2² × 3 × 5)² = (4 × 3 × 5)² = 60². Therefore, √(2⁴ × 3² × 5²) = 2² × 3 × 5 = 60.