Author name: Narender Kumar

Class 8 Maths NCERT Solutions for Ganita Prakash Part 1 Chapter 1 – A Square and a Cube provide clear and easy-to-follow solutions to the questions and activities given in the new NCERT Mathematics textbook for Class 8. This chapter introduces students to square numbers, perfect squares, square roots, cube numbers and cube roots through patterns, puzzles and mathematical exploration. Students also learn different methods for finding square roots and cube roots and explore useful patterns involving squares and cubes. The chapter is part of Ganita Prakash Part 1, the new Class 8 NCERT Mathematics textbook being used from the 2026–27 academic year. Watch Video:Class 8 Maths Ganit Praksh NCERT Solutions-1 | A Square & A Cube What You’ll Learn In – A Square and a Cube In this chapter, students will learn about: These concepts form the foundation for working with squares, cubes and roots in higher classes. Important Concepts from A Square and a Cube 1. Square Numbers A number obtained by multiplying a number by itself is called its square. For example: 52=5×5=25 Therefore, 25 is a square number. Similarly: 102=10×10=100 So, 100 is a perfect square. 2. Perfect Squares Numbers such as: 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100 are perfect squares because each can be expressed as the product of a whole number with itself. 3. Square Root The square root of a number is the number which, when multiplied by itself, gives the original number. For example: √(64) = 8​ because: 8×8=64 4. Cube Numbers A number obtained by multiplying a number by itself three times is called its cube. For example: 4=4×4×4=64 Therefore, 64 is a perfect cube. Some perfect cubes are: 1, 8, 27, 64, 125, 216, 343, 512 and 729. The textbook also explores patterns in cube numbers and asks students to identify relationships between numbers and their cubes Therefore, 64 is a perfect cube.Some perfect cubes are: 1, 8, 27, 64, 125, 216, 343, 512 and 729. The textbook also explores patterns in cube numbers and asks students to identify relationships between numbers and their cubes. 5. Cube Root The cube root of a number is the number which, when multiplied by itself three times, gives the original number. For example: Because: 5×5×5=125 Watch Video:Class 8 Maths Ganit Praksh NCERT Solutions-2 | A Square & A Cube Class 8 Ganita Prakash Chapter 1 – Figure It Out Questions The chapter contains Figure It Out questions that encourage students to apply the concepts of squares, square roots, cubes and cube roots rather than simply memorising formulas. For example, students are asked to identify numbers that are not perfect squares and investigate patterns in square and cube numbers. How to solve these questions How to Use These Class 8 Ganita Prakash Solutions Try to solve every question yourself before looking at the solution. If you cannot solve a question, read the explanation carefully and identify the mathematical concept or method being used. Then try solving the question again without looking at the answer. This approach will help you: Class 8 maths Ganita Prakash chapter 1 | A Square and A Cube | Exam Questions: Watch Full video Conclusion Class 8 Maths Ganita Prakash Part 1 Chapter 1 – A Square and a Cube introduces important concepts related to squares, cubes, square roots and cube roots. By practising the textbook questions and understanding the patterns explained in the chapter, students can develop a strong foundation in number concepts. Use the chapter-wise and question-wise solutions on Future Study Point to check your answers, understand the correct method and practise more questions.

Unique ID codes for 8.5 billion milk packets is the focus of this interesting question from Class 8 Maths Ganit Prakash Chapter 2 – Power Play. In this question, a dairy plans to produce 8.5 billion packets milk packets in a year and wants to assign a unique ID code to each packet. The challenge is to determine the minimum number of digits required so that every packet can have a different code. Question:A dairy plans to produce 8.5 billion packets of milk in a year. They want a unique ID (identifier) code for each packet. If they choose to use the digits 0–9, how many digits should the code consist of? Watch the video Solution Solution The dairy needs to produce: 8.5 billion packets We know that: 1 billion = 1,000,000,000 Therefore, 8.5 billion = 8,500,000,000 So, the dairy needs to assign a unique ID code to 8,500,000,000 packets. If code is of 1 digit,then codes generated are from 0 to 9 that are 10 codes If code is of 2 digit,then codes generated are =10 x 10 =102 See the Complete Solution Class 8 Maths – Ganit Prakash Chapter 2: Power Play This question is based on large numbers and the use of digits to create unique identifiers. It helps students understand how the number of digits changes as numbers become larger and how to determine the minimum number of digits needed to represent a large quantity. If you are studying Class 8 Maths Ganit Prakash Chapter 2 – Power Play, practise more questions involving large numbers, place value, and number representation. Subscribe to Future Study Point for more Class 8 Maths Ganit Prakash solutions, NCERT-based questions, important questions, and exam preparation videos. Watch complete Solution of Class 8 Maths Chapter 2 Power Play Similar Questions Class 8 Maths Ganit Prakash Chapter 2 Power Play Q1.Roxie has 7 dresses, 2 hats, and 3 pairs of shoes. How many different ways can Roxie dress up? (Page 26) Q2.Write the number of lotuses (in exponential form) when the pond was(i) fully covered(ii) half covered (Page 25) Q3.Estu says, “Next time I will buy a lock that has 6 slots with the letters A to Z. I feel it is safer.”How many passwords are possible with such a lock? (Page 27) Q4.Estu and Roxie came across a safe containing old stamps and coins that their great-grandfather had collected. It was secured with a 5-digit password. Since nobody knew the password, they had no option except to try every password until it opened. They were unlucky, and the lock only opened with the last password, after they had tried all possible combinations. How many passwords did they end up checking? (Page 26) Q5:Say you can fold a sheet of paper as many times as you wish. What would its thickness be after 30 folds? Make a guess. Let us find out how thick a sheet of paper will be after 46 folds. Assume that the thickness of the sheet is 0.001 cm. Q6:Which expression describes the thickness of a sheet of paper after it is folded 10 times? The initial thickness is represented by the letter-number v. (i) 10v (ii) 10 + v (iii) 2 × 10 × v (iv) 2¹⁰ (v) 2¹⁰v (vi) 10²v Q7:Express the number 32400 as a product of its prime factors and represent the prime factors in their exponential form. 8:What is (−1) 5 ? Is it positive or negative? What about (−1) 56 ? Q9:Is (−2) 4 = 16? Verify. Q10. Express the following in exponential form: (i) 6×6×6×6 (ii) y× y (iii) b×b×b×b (iv) 5×5×7×7×7 (v) 2×2×a×a (vi) a×a×a×c×c×c×c×d Class 10 Maths Most Important Questions on Real Numbers Class 10 Maths Most Important Questions Chapter 1 Real Numbers Class 10 Maths Basic Sample Paper Solution: Practise with the Complete CBSE Basic Sample Paper Solution Class 10 Maths NCERT Solutions CBSE 2026-27 Update Continue your Class 10 Maths preparation with these useful resources from Future Study Point: Class 10 Maths Chapter 1 – Real Numbers: Complete NCERT Exercise-Wise Video Solutions Class 10 Maths Chapter 2 – Polynomials: Complete NCERT Solutions for Polynomials Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables: Complete NCERT Solutions Class 10 Maths Chapter 4 Quadratic Equations: – Quadratic Equations complete NCERT video solutions Class 10 Maths Chapter 5 Arithmetic Progression: Arithmetic Progression: complete video solution 👉 Explore these resources to strengthen your concepts, revise important topics, and prepare effectively for the CBSE Board Examination 2026–27.