The NCERT Solutions for Class 8 Mathematics Part 1 Chapter 1 cover A Square and A Cube for the 2026-27 Ganita Prakash textbook. Students can download the PDF for step-by-step answers on perfect squares, square roots, perfect cubes, cube roots, factor grouping and Figure it Out questions.
- Resource: Class 8 Maths Part 1 Chapter 1 NCERT Solutions PDF.
- Chapter focus: squares, roots, cubes, taxicab numbers and factor patterns.
- Question type: in-chapter prompts and Figure it Out answers.
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Student Feedback: These solutions show the reason behind each shortcut, so students can solve square and cube pattern questions without memorising only final answers.
In This Article
Chapter 1 Solutions Overview
Class 8 Mathematics Part 1 Chapter 1 begins with the locker puzzle and then builds the ideas of square numbers, square roots, cubic numbers and cube roots. The PDF explains why square numbers have an odd number of factors, how ending digits help reject non-squares and how prime factorisation helps identify perfect squares and cubes.
The chapter also includes taxicab numbers and consecutive odd-number patterns. These solutions keep each calculation visible, so students can see how the answer follows from the method.
Key Methods for Squares and Cubes
Most questions in this chapter become simple after choosing the right test. Perfect square questions usually need factor pairs. Perfect cube questions need factor triplets. Ending-zero questions use the rule that squaring doubles the number of zeros while cubing triples it.
- Use units digits 2, 3, 7 and 8 to reject perfect squares.
- Use n squared to (n plus 1) squared gap equals 2n plus 1.
- Use prime factorisation to complete missing pairs or triplets.
- Use nearby known cubes to guess cube roots quickly.
Class 8 Maths Chapter 1 Square and Cube Video Lesson
Source: Magnet Brains on YouTube
All Chapter 1 Question Cards with Solutions
The companion question-card page gives each solved prompt with a Check Solution panel and an Expert Solution panel. Use it for quick revision before downloading the full PDF.
Open question cards: Class 8 Maths Chapter 1 step-by-step solutions
Related Class 8 Maths Part 1 Chapter 1 Resources
| Resource | Class 8 Maths Part 1 Chapter 1 Link |
|---|---|
| NCERT Book PDF | Read the official chapter PDF |
| Notes | Revise Chapter 1 with notes |
| Handwritten Notes | Open handwritten revision notes |
Class 8 Maths Part 1 NCERT Solutions for All Chapters
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1 | A Square and A Cube Solutions |
| Chapter 2 | Power Play Solutions |
| Chapter 3 | A Story of Numbers Solutions |
| Chapter 4 | Quadrilaterals Solutions |
| Chapter 5 | Number Play Solutions |
Class 8 Maths Part 1 Chapter 1 NCERT Solutions FAQs
Ques. What is covered in Class 8 Maths Part 1 Chapter 1 NCERT Solutions?
Ans. The solutions cover perfect squares, square roots, perfect cubes, cube roots, factor grouping and Figure it Out questions from A Square and A Cube.
Ques. Are these Chapter 1 solutions based on the 2026-27 NCERT book?
Ans. Yes. The PDF follows the 2026-27 NCERT Ganita Prakash Class 8 Mathematics Part 1 chapter A Square and A Cube.
Ques. Why do square numbers have an odd number of factors?
Ans. A square number has one middle factor that pairs with itself, so its factor count becomes odd.
Ques. Does the PDF include cube root questions?
Ans. Yes. It includes cube roots of 27000, 10648 and other perfect cubes, with factor-triplet methods.
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