Class 8 Maths Part 1 Chapter 1 PDF: A Square and a Cube (Ganita Prakash)

Class 8 Maths Part 1 Chapter 1, A Square and a Cube, opens Ganita Prakash Part I (2026-27) with Queen Ratnamanjuri’s 100-locker puzzle, where only locker numbers with an odd number of factors—the perfect squares 1, 4, 9, 16, …, 100—remain open.

What Class 8 Maths Chapter 1 Covers

1.1 Square Numbers and Square Roots explore patterns in perfect squares (units digits, even number of trailing zeros, sums of consecutive odd numbers, and consecutive triangular numbers) and finding square roots by prime factorisation.

1.2 Cubic Numbers and Cube Roots cover perfect cubes, Hardy–Ramanujan taxicab numbers (such as 1729 = 1³ + 12³ = 9³ + 10³), expressing cubes as sums of consecutive odd numbers, successive differences and cube roots.

1.3 A Pinch of History and Square Pairs! trace square-root extraction in ancient India (Āryabhaṭa) and end with the Square Pairs puzzle arranging 1 to 17 so every adjacent pair sums to a square.

Exercises in Chapter 1

• Figure it Out exercise sets after each major section, with complete answer keys at the end of the chapter.

Read Class 8 Maths Chapter 1 Online

More Chapters

• Next: Chapter 2: Power Play
• Hindi medium: Class 8 Maths Part 1 Chapter 1 PDF in Hindi (Ganita Prakash)
• All Maths chapters and the other Class 8 books: Class 8 NCERT books 2026-27
• All Class 1 to 12 NCERT Textbooks: NCERT Books PDF (Class 1–12)
• Every book chapter by chapter: NCERT chapter wise PDF

FAQ

Why do only square-numbered lockers stay open in the 100-locker puzzle?
Because factors of a number come in pairs except when the number is a perfect square, giving perfect squares an odd number of factors.

What is a taxicab number in Class 8 Maths Chapter 1?
A number that can be expressed as the sum of two positive cubes in more than one way, such as 1729 = 1³ + 12³ = 9³ + 10³.

Updated 2026–27 NCERT Class 8 Books & Chapter-Wise PDFs

Looking for all chapters and the latest 2026–27 NCF NCERT textbooks for Class 8? Open any chapter below to download its official PDF or read our Read Online & Notes study guide, or visit the complete NCERT Class 8 Books PDF (2026–27 Main Page) for all subjects or All NCERT Books PDF (Class 1 to 12).