Class 8 Mathematics Chapter 1 A Square and A Cube is a high-frequency chapter in the CBSE Class 8 Mathematics exam. These class 8 maths handwritten notes chapter 1 A Square and A Cube follow the 2026-27 NCERT and cover square numbers and perfect squares, patterns in the units digit of squares, squares as sums of odd numbers..
- CBSE Class 8 Weightage: a scoring chapter in the Mathematics paper, asked in short and long answers.
- What the notes cover: square numbers and perfect squares, patterns in the units digit of squares, squares as sums of odd numbers, square roots and their meaning.
- Best for: quick revision before Class 8 exams and a strong base for Class 9.
You can read the complete class 8 maths handwritten notes for A Square and A Cube, with key terms, boxed definitions, and quick revision points, in the PDF below.
These handwritten notes are written by subject teachers, mapped to the 2026-27 NCERT, and checked against the last five years of CBSE Class 8 Mathematics papers.
What the A Square and A Cube Handwritten Notes Cover
This chapter is about square numbers and cube numbers. You learn how a number multiplied by itself gives a square, and multiplied by itself three times gives a cube. You also find square roots and cube roots and spot patterns in these numbers.
- Square numbers and perfect squares
- Patterns in the units digit of squares
- Squares as sums of odd numbers
- Square roots and their meaning
- Prime factorisation to test perfect squares
- Cube numbers and perfect cubes
- Cube roots using prime factorisation
- Taxicab numbers like 1729
- Successive differences of squares and cubes
A Square and A Cube Self-Assessment Quiz
Try these quick questions after you read the notes. Tap each question to check your answer. They cover the points CBSE asks most often.
Which number is a perfect square?
(a) 27 (b) 48 (c) 64 (d) 50
Answer: (c) 64 - because 8 times 8 is 64
A number ending in which digit cannot be a perfect square?
(a) 4 (b) 6 (c) 7 (d) 9
Answer: (c) 7 - squares never end in 2, 3, 7 or 8
What is the square root of 81?
(a) 7 (b) 8 (c) 9 (d) 27
Answer: (c) 9 - since 9 times 9 is 81
Which number is a perfect cube?
(a) 9 (b) 27 (c) 100 (d) 50
Answer: (b) 27 - since 3 times 3 times 3 is 27
1729 is famous because it is the smallest number that is
(a) a perfect square (b) a perfect cube (c) the sum of two cubes in two ways (d) a prime
Answer: (c) the sum of two cubes in two ways - 1 cubed plus 12 cubed and 9 cubed plus 10 cubed
The cube root of 125 is
(a) 5 (b) 15 (c) 25 (d) 3
Answer: (a) 5 - since 5 times 5 times 5 is 125
A Square and A Cube Topic-wise Weightage for CBSE Class 8 Mathematics
Some parts of this chapter are asked more often than others. The table below shows which sub-topics to revise first, based on recent CBSE Class 8 question trends.
| Sub-topic | Weightage | CBSE Frequency |
|---|---|---|
| Square numbers and their patterns | High | asked often |
| Square roots by prime factorisation | High | asked often |
| Cube numbers and cube roots | High | asked often |
| Estimating square roots of larger numbers | Medium | asked sometimes |
| Squares as sums of consecutive odd numbers | Medium | asked sometimes |
| Taxicab numbers and history | Low | asked rarely |
Key Terms and Ideas in A Square and A Cube
These are the terms and ideas the exam asks about most. Learn each one so you can define it and use it in your answers.
| Term / Idea | What it means |
|---|---|
| Square number | a number got by multiplying a number by itself, like 25 = 5 times 5 |
| Perfect square | the square of a natural number, such as 1, 4, 9, 16, 25 |
| Square root | the number that gives the square when multiplied by itself, root of 49 is 7 |
| Odd factors rule | only square numbers have an odd number of factors |
| Units digit test | a number ending in 2, 3, 7 or 8 is never a perfect square |
| Cube number | a number got by multiplying a number by itself three times, like 27 = 3 times 3 times 3 |
| Cube root | the number that gives the cube when multiplied by itself three times, cube root of 27 is 3 |
| Prime factor grouping | a number is a square if its prime factors split into two equal groups, a cube if into three equal groups |
| Taxicab number | a number that is the sum of two cubes in two different ways, such as 1729 |
How Collegedunia's Handwritten Notes Help You Revise A Square and A Cube
These notes are made for the night before the exam. They keep the facts short and easy to scan. Collegedunia maps every point to the 2026-27 NCERT.
- Clear handwriting: each topic is written in neat, easy-to-read handwriting.
- Boxed key terms: the main terms and definitions are boxed by hand for fast recall.
- Diagrams and tables: simple hand-drawn tables and charts make ideas clear.
- Colour-coded headings: new sub-topics stand out, so you find any section in seconds.
How to Use These Handwritten Notes for Class 8 Mathematics Revision
Use these class 8 maths handwritten notes in two passes. Read them slowly once for the full chapter. Then, near the exam, read only the boxes and key terms for a fast recall.
- Read the notes once with the NCERT chapter open beside you.
- Say each key term and idea in your own words.
- Practise one long-answer question from a past paper.
- On the last day, revise only the key terms and the boxes.
Class 8 Mathematics Handwritten Notes for All Chapters
The table below links the class 8 maths handwritten notes for every chapter. Use it to jump to any other chapter's notes.
| Chapter | Resource |
|---|---|
| Chapter 1 | A Square and A Cube Handwritten Notes |
| Chapter 2 | Power Play Handwritten Notes |
| Chapter 3 | A Story of Numbers Handwritten Notes |
| Chapter 4 | Quadrilaterals Handwritten Notes |
| Chapter 5 | Number Play Handwritten Notes |
| Chapter 6 | We Distribute, Yet Things Multiply Handwritten Notes |
| Chapter 7 | Proportional Reasoning-1 Handwritten Notes |
A Square and A Cube Class 8 Mathematics Handwritten Notes FAQs
Ques. Where can I download A Square and A Cube Class 8 Mathematics Handwritten Notes PDF?
Ans. You can download the A Square and A Cube Class 8 Mathematics Handwritten Notes PDF directly from this page. Both the Normal and HD versions are free.
Ques. Are these handwritten notes aligned with the 2026-27 NCERT?
Ans. Yes. These notes follow the current 2026-27 syllabus for Class 8 Mathematics. The difference between a square number and a cube number in simple words.
Ques. How many pages is the Class 8 Mathematics A Square and A Cube Handwritten Notes PDF?
Ans. The notes run about 20 pages. They cover the full chapter with key terms, hand-drawn boxes, and a short self-assessment quiz.
Ques. What is the main idea of the 8th standard Mathematics chapter A Square and A Cube?
Ans. The chapter shows how to build square and cube numbers and how to reverse them using square roots and cube roots. It also teaches you to test whether a number is a perfect square or perfect cube using prime factorisation and digit patterns.
Ques. Are these A Square and A Cube notes enough for the CBSE Class 8 exam?
Ans. Yes, for revision. The Collegedunia handwritten notes cover every key point and exam term. Read them with the NCERT chapter and practise past questions.
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