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NCERT Solutions
Class 8
Maths
A Square and a Cube

NCERT Solutions for Class 8 Maths Chapter 1 - A Square and a Cube

The NCERT Solutions for Class 8 Maths Chapter 1—A Square and A Cube has been developed in such a way that they provide a clear and structured way to understand square and cube numbers along with their roots for all Class 8 students. This chapter forms the basis for developing numerical skills in Class 8 Mathematics, which helps develop a student’s ability to solve problems accurately and confidently.

These solutions are created based on the NCERT Curriculum, based on the latest syllabus issued by the National Council Of Educational Research And Training (NCERT) and also the patterns of questions as per the CBSE Examination. The concepts covered in these solutions will be explained step by step and will clarify how to study and revise each concept successfully.

1.0NCERT Solutions for Class 8 Maths Chapter 1 PDF Download


Students can download the A Square and a Cube Class 8 PDF with answers from the table below. The NCERT Solutions for Class 8 Maths Chapter 1 – A Square and a Cube PDF are meticulously prepared by ALLEN’s expert faculty members, who possess strong subject expertise and a deep understanding of the latest NCERT and CBSE curriculum. These solutions are designed to help students understand concepts clearly and perform confidently in examinations.

NCERT Solutions for Class 8 Maths Chapter 1 - A Square and a Cube

2.0Quick Insights About the Chapter – A Square and a Cube

This chapter establishes the fundamental concepts related to number patterns and powers, which are essential for developing numerical understanding in mathematics.

  • The definition of square numbers and cube numbers, along with an explanation of how they are formed through repeated multiplication.
  • Identification of perfect squares and perfect cubes using number patterns and properties.
  • Understanding the properties of square numbers, including patterns related to even and odd numbers and the possible last digits of perfect squares.
  • Methods to find square roots and cube roots, primarily using the prime factorisation technique.
  • Recognition of number patterns to determine whether a given number is a perfect square or a perfect cube.
  • Application of square and cube concepts to solve numerical and reasoning-based problems.

3.0Benefits of NCERT Solutions Class 8 Maths Chapter 1

Students can take advantage of NCERT Solutions for Class 8 Maths Chapter 1 - A Square and a Cube to gain a strong mathematical knowledge base to perform better in exams.

  1. Conceptual Clarity: - They provide an in-depth explanation of square numbers, cube numbers, and their roots in a simple format to help students grasp these concepts easily.
  2. Conformance to NCERT and CBSE Curriculum: - All solutions conform entirely to the latest NCERT syllabus and the CBSE examination formats.
  3. Mathematical Problem Solving Skills: - The solutions explain how to properly approach numerical problems and logical reasoning questions through step-by-step examples.
  4. Exam Preparation Tools: - By practising NCERT questions with the correct answers, students will feel more at ease with their speed, accuracy, and confidence during exams.
  5. Foundation for Future Topics: - Using square and cube numbers as a foundation prepares students for subjects at a more advanced level, such as Algebra, Exponents, and Number Systems.
  6. A Resource for Study and Reinforcement: - The well-organized layouts of the solutions create an easy reference for independent study/reviewing when questions arise.

Table of Contents


  • 1.0NCERT Solutions for Class 8 Maths Chapter 1 PDF Download
  • 2.0Quick Insights About the Chapter – A Square and a Cube
  • 3.0Benefits of NCERT Solutions Class 8 Maths Chapter 1

Frequently Asked Questions

A square number can be defined as the result of multiplying an integer by itself. The number 16 is an example of a square number; it can be expressed as 4 x 4.

A number is a perfect square if its prime factors can be grouped into pairs. If it is possible to group all of the prime factors into pairs, then the number is a perfect square.

In Class 8, students will primarily use the prime factorisation method to find the square root of a perfect square number.

A number becomes a cube only when it has been multiplied by itself 3 times. An example of a cube is the number 27, which can be expressed through the formula 3 x 3 x 3.

Because Chapter 1 lays the groundwork for a lot of later lessons, and since these concepts are often asked about in questions involving numerical values, a good grasp of the principles of squares and cubes leads to higher marks in examinations.

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