A Square and A Cube
CBSE · Class 8 · Mathematics
Summary of A Square and A Cube for CBSE Class 8 Mathematics. Key concepts, important points, and chapter overview.
Interactive on Super Tutor
Studying A Square and A Cube? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for chapter summary and more.
1,000+ Class 8 students started this chapter today
Overview
Squares and cubes are important number patterns in arithmetic and geometry. A square number is formed by multiplying a number by itself, and a cube number is formed by multiplying a number by itself three times. The chapter also connects these ideas to locker puzzles, factor pairs, odd numbers, unit
Key Concepts
A number that can be written
A number that can be written as n × n = n² is called a square number. Examples include 1, 4, 9, 16, and 25.
A locker toggled an odd number
A locker toggled an odd number of times ends up open; otherwise it ends up closed. The number of times a locker is toggled equals the number of factor
The lockers left open are
The lockers left open are the square numbers. The first five lockers toggled exactly twice are the prime numbers, which give the passcode 2-3-5-7-11.
Squares can have units digits 0
Squares can have units digits 0, 1, 4, 5, 6, or 9 only. A number ending in 2, 3, 7, or 8 is definitely not a square. A number ending in 0, 1, 4, 5, 6,
The difference between consecutive squares forms
The difference between consecutive squares forms the sequence of odd numbers. The sum of the first n odd numbers equals n². Every square is a sum of s
Learning Objectives
- Understand what square numbers and cube numbers mean
- Identify perfect squares using factor pairs and odd-number patterns
- Use units digits to rule out numbers that cannot be squares
- Find square numbers by adding successive odd numbers
- Understand cube numbers through multiplication and prime factorisation
Frequently Asked Questions
What are the important topics in A Square and A Cube for CBSE Class 8 Mathematics?
How to score full marks in A Square and A Cube — CBSE Class 8 Mathematics?
Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for A Square and A Cube
Practice Quiz
Test yourself with a quick quiz
Important Questions
Practice with board exam-style questions
Revision Notes
Key points for last-minute revision
Formula Sheet
All formulas in one place
Concept Maps
See how topics connect visually
Study Plan
Step-by-step plan to ace this chapter
Flashcards
Quick-fire cards for active recall
Syllabus
What topics to cover
NCERT Solutions
Every textbook question solved step by step
For serious students
Get the full A Square and A Cube chapter — for free.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for CBSE Class 8 Mathematics.