NCERT MCQ Solutions for Class 8 Maths Ganita Prakash Chapter 1 A Square and A Cube updated for Session 2025–26. Ganita Prakash Objective Questions help students practice better. All answers are correct and easy to understand. Each question is solved with simple steps. NCERT 8th Maths chapter 1 covers square and cube numbers. Roots and patterns are also explained. These MCQs improve speed and accuracy. Students can revise quickly before exams. The solutions are useful for the Session 2025–26 syllabus.
Class 8 Maths NCERT Solution
Class 8 Mathematics MCQ
Class 8 All Subjects MCQ
A Square and A Cube Class 8 Maths Chapter 1 MCQ Online Test
Q1. What type of numbers will remain open in the 100-locker puzzle described in the will?
Q2. According to the puzzle, how can Khoisnam claim the entire inheritance of ratnas?
Q3. What determines if a locker remains open or closed in the puzzle?
Q4. The number of times a locker is toggled is equivalent to what?
Class 8 Maths Chapter 1 A Square and A Cube MCQs
Class 8 Maths Ganita Prakash Chapter 1 begins with a clever puzzle involving 100 lockers and 100 people, where each person toggles lockers based on a pattern. Through this, we learn that the lockers left open at the end are those whose numbers are perfect squares, like 1, 4, 9 and so on. This is because square numbers have an odd number of factors. Understanding this concept helps us clearly identify square numbers and their unique properties. In MCQs, we often face questions like “Which of these is a square number?” or “Which locker remains open?”. Practicing such MCQs improves our speed, logic and clarity in number patterns, which is required for scoring well in competitive tests.
Q5. What is the passcode to the fortune in the safe?
Q6. Which of the following numbers is an example of a perfect square?
Q7. What notation is used to represent ‘n squared’?
Q8. Which of the following digits cannot be the units digit of a perfect square?
Learning Square Roots with Class 8 Maths Chapter 1 MCQs
Class 8 Maths Ganita Prakash Chapter 1 teaches us how to find square roots through different methods: by listing square numbers, subtracting consecutive odd numbers and prime factorization. We also explore how to estimate square roots of large numbers and how square roots always have both positive and negative values. These ideas not only build our conceptual foundation but also help in solving MCQs that ask for square roots, identification of perfect squares or number estimation. Practicing such MCQs enables us to choose the correct option quickly and improves our number sense and confidence during exams.
Q9. What is observed about the number of zeros at the end of a perfect square?
Q10. What is the sum of the first ‘n’ odd numbers?
Q11. How can you determine if a number is a perfect square by successively subtracting odd numbers?
Perfect Cubes based MCQs in Class 8 Maths
After squares, Class 8 Maths Ganita Prakash Chapter 1 dives into cubes—numbers formed by multiplying a number by itself three times. We learn how to recognize perfect cubes, calculate cube roots and use prime factorization to check if a number is a cube. Fascinating stories like Ramanujan’s taxicab number (1729) make the topic more engaging. MCQs on cubes often test our understanding of cube patterns, cube roots and properties of numbers. Practicing cube-related MCQs helps students apply logic quickly and avoid confusion, especially when dealing with large numbers or abstract cube patterns in higher math.
Q14. How many integer square roots does every perfect square have?
Q15. What does the symbol √ denote?
Q16. What is a “taxicab number”?
Patterns, Observations and Historical Insight based MCQs
Class 8 Maths Ganita Prakash Chapter 1 emphasizes identifying patterns in square and cube numbers—such as last digits, number of zeroes and differences between consecutive squares and cubes. It even connects math with history by showing how ancient mathematicians studied squares and cubes. These patterns are commonly tested in MCQs, such as “Which number cannot be a square based on its last digit?” or “Which number is a cube based on its factors?”. Regular practice with MCQs makes it easier to spot such patterns instantly and gives an edge in problem-solving, making mathematics more enjoyable and less intimidating for students.
Q17. How is a number like 3375 determined to be a perfect cube using prime factorization?
Q19. Which term was used in ancient Sanskrit works for the square power?
Q20. What was the ancient Indian Sanskrit word for “root of a plant” that was also used for mathematical operations of taking roots?
Why is it important to practice Class 8 Maths Ganita Prakash Chapter 1 MCQ?
Practicing MCQs from Class 8 Maths Ganita Prakash Chapter 1 helps students understand perfect squares and cubes through active recall and quick decision-making. A perfect square is a number like 1, 4, 9, which comes from multiplying a number by itself. Similarly, cubes like 8, 27 and 64 are formed by multiplying a number three times.
The MCQs in this chapter often test how well students can recognize these numbers, spot patterns and apply factor-based logic. By solving such questions regularly, students build speed and accuracy. They also get better at eliminating wrong choices based on units digits or properties of numbers.
This repeated exposure deepens their understanding of number behavior, primes and multiplication patterns, which is important for advanced chapters in algebra and geometry. So, regular MCQ practice strengthens both conceptual clarity and exam confidence.
How do Class 8 Maths Ganita Prakash Chapter 1 MCQ help in improving square root and cube root skills?
Class 8 Maths Chapter 1 introduces methods like prime factorization, estimation and repeated subtraction to find square roots and cube roots. MCQs related to these topics test a student’s ability to quickly identify whether a number is a perfect square or cube and find its root. When students regularly practice such MCQs, they develop mental shortcuts to check answers quickly.
For example, recognizing that 576 is a perfect square and its square root is 24 becomes second nature. Similarly, they learn to identify cube roots like ³√729 = 9 just by looking. Practicing Class 8 Maths Ganita Prakash Chapter 1 MCQ also trains students to estimate roots when numbers are not perfect squares or cubes. This combination of logic and estimation builds number sense and problem-solving skills, which are essential in both academic and competitive exams.
What kind of number patterns can be mastered by solving Class 8 Maths Ganita Prakash Chapter 1 MCQ?
Class 8 Ganita Prakash Chapter 1 is full of number patterns—like how square numbers increase by consecutive odd numbers (1, 3, 5…) or how perfect cubes relate to the sum of grouped odd numbers. MCQs often challenge students to apply these patterns in a timed setting.
For example, an MCQ may ask which number cannot be a square based on its last digit, or which cube falls between 100 and 200. When students solve Class 8 Maths Ganita Prakash Chapter 1 MCQ, they naturally begin to observe how certain digits never appear at the end of square numbers or how cube numbers are spaced. These patterns save time during exams and reduce the need for full calculations. Regular practice sharpens the eye for such details and helps students become better at identifying tricks, shortcuts and hidden relationships in numbers.
In what way do Class 8 Maths Ganita Prakash Chapter 1 MCQ help in building the base for higher math topics?
Class 8 NCERT Maths Chapter 1 sets the foundation for topics like algebra, geometry and exponents. It introduces factorization, visual understanding of squares, cubes and how to reverse operations using roots. MCQs based on these concepts prepare students for future math challenges. For instance, identifying whether a number is a square using prime factor groups becomes important later in solving quadratic equations. Practicing Class 8 Maths Ganita Prakash Chapter 1 MCQ ensures that students build this foundation early.
The format of MCQs also teaches them how to think fast and analyze patterns efficiently—skills that are useful in all areas of math. This chapter makes abstract ideas more concrete and MCQ practice turns these ideas into habits. It helps students bridge basic arithmetic with logical reasoning, which is key in math success ahead.
What are some tips to score better in Class 8 Maths Ganita Prakash Chapter 1 MCQ?
To do well in MCQs from Class 8 Ganita Prakash Chapter 1, start by memorizing square numbers up to 30² and cube numbers up to 20³. Recognize common units digits for squares (0, 1, 4, 5, 6, 9) and cubes (0 to 9). Understand how to find roots using factorization and estimation. While solving Class 8 Maths Chapter 1 MCQ, don’t try to solve every question through long calculation—use elimination and shortcut methods. For example, if a number ends with 2, it cannot be a perfect square. Also, learn to identify prime numbers quickly, as they appear often in factor-related questions. Practice consistently with varied MCQ types: direct value checks, property-based or pattern-based. The more you solve, the faster your brain recognizes the logic, making it easier to pick the right option under exam pressure.
