Chapter 1 · Class 8 CBSE · MCQ Test
Squares, Cubes & Their Roots MCQ Test — Class 8 CBSE
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Squares, Cubes & Their Roots — MCQ Questions
1Which of the following numbers, based on its unit digit, can definitively be stated as NOT a perfect square?
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Answer: 6723
Hint: Recall the unit digits that perfect squares can never end with.
Solution:
A perfect square cannot end with the digits 2, 3, 7, or 8.
Let's check the unit digit of each option:
3136 ends in 6 (can be a perfect square, e.g., 56²).
4096 ends in 6 (can be a perfect square, e.g., 64²).
5249 ends in 9 (can be a perfect square, e.g., 73²).
6723 ends in 3. Since a perfect square cannot end in 3, 6723 cannot be a perfect square.
2Which statement is TRUE about the number of non-perfect square numbers between n² and (n+1)² for any natural number 'n'?
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Answer: It is always 2n.
Hint: Consider a small example, like the numbers between 2² and 3².
Solution:
Let's take an example: For n=2, n² = 4 and (n+1)² = 9.
The numbers between 4 and 9 are 5, 6, 7, 8. There are 4 non-perfect square numbers.
Using the formula 2n, we get 2 × 2 = 4.
This property states that there are 2n non-perfect square numbers between the squares of 'n' and '(n+1)'.
3Which of the following represents the sum of the first 6 odd natural numbers?
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Answer: 36
Hint: Remember the pattern relating the sum of consecutive odd numbers to square numbers.
Solution:
The sum of the first 'n' odd natural numbers is equal to n².
In this case, we need the sum of the first 6 odd natural numbers, so n = 6.
Therefore, the sum is 6².
6² = 36.
4Ravi tried to find the square root of 196 by prime factorization. His steps are shown below: 1. 196 = 2 × 98 2. = 2 × 2 × 49 3. = 2 × 2 × 7 × 7 4. He then wrote, √196 = 2 × 7 = 14. Which of the following statements about Ravi's solution is correct?
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Answer: Ravi correctly applied the prime factorization method to find the square root.
Hint: Review the steps involved in finding the square root using prime factorization.
Solution:
The prime factorization of 196 is indeed 2 × 2 × 7 × 7.
To find the square root, we group the prime factors into pairs: (2 × 2) and (7 × 7).
Then, we take one factor from each pair and multiply them: 2 × 7 = 14.
All of Ravi's steps and his conclusion are correct according to the prime factorization method for square roots.
5A Pythagorean triplet consists of three positive integers a, b, and c, such that a² + b² = c². Which of the following sets of numbers forms a Pythagorean triplet?
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Answer: (8, 15, 17)
Hint: Substitute the values into the formula a² + b² = c² for each option.
Solution:
We need to check which set satisfies the condition a² + b² = c².
A) (3, 4, 6): 3² + 4² = 9 + 16 = 25. But 6² = 36. So, 25 ≠ 36.
B) (8, 15, 17): 8² + 15² = 64 + 225 = 289. And 17² = 289. So, 289 = 289. This is a Pythagorean triplet.
C) (6, 8, 9): 6² + 8² = 36 + 64 = 100. But 9² = 81. So, 100 ≠ 81.
D) (7, 24, 26): 7² + 24² = 49 + 576 = 625. But 26² = 676. So, 625 ≠ 676.
6Meena tried to find the square root of 49 using the repeated subtraction method. She wrote: 1. 49 - 1 = 48 2. 48 - 3 = 45 3. 45 - 5 = 40 4. 40 - 7 = 33 5. 33 - 9 = 24 6. 24 - 11 = 13 7. 13 - 13 = 0 She concluded that √49 = 7. Which statement best describes Meena's method?
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Answer: Meena correctly applied the repeated subtraction method, and her conclusion is correct.
Hint: Recall the steps for finding a square root using the repeated subtraction method.
Solution:
The repeated subtraction method involves subtracting consecutive odd numbers (1, 3, 5, 7, ...) from the given number until the result is 0.
The number of subtractions performed is the square root of the original number.
Meena correctly subtracted 1, 3, 5, 7, 9, 11, and 13, and reached 0 in 7 steps.
Therefore, her application of the method and her conclusion that √49 = 7 are correct.
7Which of the following statements about square numbers is TRUE?
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Answer: The square of a proper fraction is always smaller than the fraction itself.
Hint: Consider examples for each statement. For a proper fraction, its value is between 0 and 1.
Solution:
A) False. A perfect square ending in zeros must have an even number of zeros (e.g., 10² = 100, 100² = 10000).
B) False. The square of an odd number is always an odd number (e.g., 3² = 9, 5² = 25).
C) False. The square of a prime number is usually a composite number (e.g., 3 is prime, but 3² = 9 is composite).
D) True. If 'x' is a proper fraction (0 < x < 1), then multiplying 'x' by itself (x²) results in a smaller number than 'x' (e.g., (1/2)² = 1/4, and 1/4 < 1/2; (3/4)² = 9/16, and 9/16 < 3/4).
8Without actually calculating, between which two consecutive integers does √110 lie?
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Answer: 10 and 11
Hint: Identify the perfect squares closest to 110.
Solution:
Find the perfect square just below 110: 10² = 100.
Find the perfect square just above 110: 11² = 121.
Since 100 < 110 < 121, it means that √100 < √110 < √121.
Therefore, 10 < √110 < 11. The square root of 110 lies between 10 and 11.
9What is the smallest number by which 363 must be multiplied to get a perfect square?
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Answer: 3
Hint: Use prime factorization to find any prime factors that are not in pairs.
Solution:
First, find the prime factorization of 363.
363 = 3 × 121
= 3 × 11 × 11
Now, group the prime factors into pairs: 3 × (11 × 11).
The factor 3 is left unpaired. To make 363 a perfect square, it must be multiplied by 3 to complete the pair for the factor 3.
So, 363 × 3 = 1089, which is 33².
10A square garden has an area of 625 square meters. If a gardener walks along its boundary twice, how much total distance does he cover?
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Answer: 200 meters
Hint: First, find the side length of the square garden from its area. Then, calculate the perimeter and multiply by the number of rounds.
Solution:
The area of a square is given by the formula: Area = side².
Given Area = 625 m², so side² = 625.
To find the side length, calculate the square root of 625: side = √625 = 25 meters.
The distance covered in one round is the perimeter of the square: Perimeter = 4 × side = 4 × 25 = 100 meters.
The gardener walks along its boundary twice, so the total distance covered is 2 × Perimeter.
Total distance = 2 × 100 = 200 meters.
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Tips for Squares, Cubes & Their Roots MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Squares, Cubes & Their Roots MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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