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Important Questions and Answers for Class 8 Maths Chapter 1 A Square And A Cube 2025-26

Q: 1. What are the most important questions to practice for Class 8 Maths Chapter 1, “A Square and a Cube”?

Focus on squares, cubes, and their properties, including finding square roots, cube roots, and short/long-answer questions based on number patterns. Practice MCQs, short, and case-based questions often found in class 8 maths chapter 1 a square and a cube question answer sets and sample papers for best results.

Q: 2. How do I structure long answers for full marks in this chapter?

Start with a clear definition or formula, write each calculation or logic step neatly, and use marking keywords. Underline answers and key statements. For a 3- or 5-mark question, ensure at least three distinct steps or value points as per the marks allotted.

Q: 3. Which subtopics from “A Square and a Cube” should I revise first for exams?

Begin with these high-weightage subtopics:Properties of squares and cubesFinding square and cube rootsIdentifying perfect squares/cubesSimple application numericalsPractice related class 8 maths chapter 1 extra questions PDF and worksheet sets for a quick revision.

Q: 4. How can I get a reliable PDF of important questions with answers for this chapter?

You can download a free a square and a cube class 8 worksheet PDF or class 8 maths chapter 1 extra questions PDF from Vedantu’s resources. These contain exam-focused questions with stepwise answers, formatted for quick revision and offline practice.

Q: 5. What are common mistakes to avoid in “A Square and a Cube” exam questions?

Common errors include:Forgetting to write steps when finding rootsMisunderstanding between squares and cubesIgnoring marking keywordsMissing units in answersAlways show your working and highlight final answers clearly.

Q: 7. What is the best way to practice exam-focused questions from this chapter quickly?

Use the a square and a cube class 8 sample paper and worksheet sets for fast practice. Time yourself for each section—MCQs, short, and long answers. Mark areas with mistakes, then review class 8 maths chapter 1 a square and a cube question answer notes for quick improvement.

Practice with A Square and a Cube Class 8 Worksheet PDF and CBSE-Oriented Answer Keys

Find the most useful class 8 maths chapter 1 a square and a cube question answer right here. This page covers Important Questions Class 8 Maths Chapter 1 A Square And A Cube, matched to your syllabus and exam needs. Each question is prepared by experienced teachers and follows the CBSE guidelines for 2025–26.

This chapter helps you understand squares and cubes with clear examples and explanations. You can also practice using the a square and a cube class 8 worksheet and download these worksheets as PDF for extra practice. The questions cover MCQs, short answers, and long answers, making revision simple and complete.

Every answer includes marking keywords and stepwise solutions. Practicing these Vedantu’s Important Questions with Answers will help you score better and avoid common mistakes in exams. Click the download link to get your free Important Questions PDF and start preparing today.

Practice with A Square and a Cube Class 8 Worksheet PDF and CBSE-Oriented Answer Keys

1. Multiple choice questions.

Q1. Which of the following numbers is a perfect square?

(a) 32
(b) 49
(c) 50
(d) 84

Answer: (b) 49

Q2. What is the cube of 4?

(a) 12
(b) 16
(c) 64
(d) 81

Answer: (c) 64

Q3. The prime factorisation of a perfect cube will have every prime appearing in multiples of:

(a) 2
(b) 3
(c) 4
(d) 5

Answer: (b) 3

Q4. Which of these numbers cannot be a perfect square?

(a) ends with 1
(b) ends with 9
(c) ends with 2
(d) ends with 6

Answer: (c) ends with 2

Q5. The smallest perfect square divisible by 4, 9, and 10 is:

(a) 180
(b) 900
(c) 100
(d) 400

Answer: (b) 900

2. Very Short Answer (VSA).

Q1. What is a perfect cube? Give an example.

Answer: A perfect cube is a number obtained by multiplying a whole number by itself three times. For example, $8 = 2 \times 2 \times 2$ is a perfect cube.

Q2. Write the cube of 7.

Answer: The cube of 7 is $7 \times 7 \times 7 = 343$.

Q3. What is the special property of a perfect square related to its number of factors?

Answer: A perfect square has an odd number of factors because the square root pairs with itself and is counted only once.

Q4. Which digit cannot be in the unit's place of a perfect square?

Answer: The digits 2, 3, 7, or 8 cannot be in the unit’s place of a perfect square.

Q5. What is the cube root of 27?

Answer: The cube root of 27 is 3, as $3 \times 3 \times 3 = 27$.

3. Short Answer Questions.

Q1. Explain how you can tell if 156 is a perfect square using prime factorisation.

Answer: Prime factorising 156 gives $2 \times 2 \times 3 \times 13$. To be a perfect square, all primes must be paired. Here, 13 has no pair, so 156 is not a perfect square.

Q2. Describe the pattern of units digits in perfect squares as per the chapter.

Answer: According to the chapter, perfect squares can only end with the digits 0, 1, 4, 5, 6, or 9, and never with 2, 3, 7, or 8. This helps to quickly check if a number can be a square.

Q3. Find the smallest number that must be multiplied with 1323 to make it a perfect cube.

Answer: Prime factorisation: $1323 = 3 \times 3 \times 3 \times 7 \times 7$. One more 7 needed to group in triples. So, multiply 1323 by 7 to get $3^3 \times 7^3 = 9261$, a perfect cube.

Q4. How can you use successive subtraction of odd numbers to check if 25 is a perfect square?

Answer: Subtract successive odd numbers from 25:

25 - 1 = 24
24 - 3 = 21
21 - 5 = 16
16 - 7 = 9
9 - 9 = 0

Since we reach zero, 25 is a perfect square.

Q5. If $a^2 = 225$, find the value of $a$. Show steps.

Answer:

$a^2 = 225$
Take square root on both sides: $a = \sqrt{225}$
$\sqrt{225} = 15$

So, $a = 15$.

4. True or False Questions.

Q1. The cube of any negative number is positive.

Answer: False.

Q2. There is no perfect cube that ends with 8.

Answer: False.

Q3. The square of a prime number always has exactly three factors.

Answer: True.

Q4. A number with an even number of factors cannot be a perfect square.

Answer: True.

Q5. The cube root of 1000 is 10.

Answer: True.

3. Fill in the Blanks Questions.

Q1. The side of a square with area 144 sq. units is ____ units.

Answer: 12

Q2. The units digit of any perfect square is never ____ or ____.

Answer: 2; 3

Q3. A perfect cube can be written as the sum of ____ consecutive odd numbers.

Answer: n (where n is the number whose cube it is)

Q4. The first perfect cube greater than 100 is ____.

Answer: 125

Q5. The value of $36^2$ is ____.

Answer: 1296

Why Learning A Square and A Cube is Valuable for Students

Understanding square and cube numbers helps students spot patterns in mathematics. Practice with class 8 maths chapter 1 a square and a cube question answer using worksheet pdfs or printable activities improves concept clarity, making foundational ideas strong for higher studies.

Solving a square and a cube class 8 worksheets encourages smart thinking and stepwise solving. Students get to work on sample paper patterns and extra questions, much like those in class 8 maths chapter 1 extra questions pdf, which helps strengthen their basics and logical reasoning.

Regular practice with notes or a square and a cube class 8 pdf gives students easy revision and better marks. Exploring concepts like a square and a cube class 8 figure it out develops confidence in tackling new types of math problems in exams and life.

FAQs on Important Questions and Answers for Class 8 Maths Chapter 1 A Square And A Cube 2025-26

1. What are the most important questions to practice for Class 8 Maths Chapter 1, “A Square and a Cube”?

Focus on squares, cubes, and their properties, including finding square roots, cube roots, and short/long-answer questions based on number patterns. Practice MCQs, short, and case-based questions often found in class 8 maths chapter 1 a square and a cube question answer sets and sample papers for best results.

2. How do I structure long answers for full marks in this chapter?

Start with a clear definition or formula, write each calculation or logic step neatly, and use marking keywords. Underline answers and key statements. For a 3- or 5-mark question, ensure at least three distinct steps or value points as per the marks allotted.

3. Which subtopics from “A Square and a Cube” should I revise first for exams?

Begin with these high-weightage subtopics:

Properties of squares and cubes
Finding square and cube roots
Identifying perfect squares/cubes
Simple application numericals

Practice related class 8 maths chapter 1 extra questions PDF and worksheet sets for a quick revision.

4. How can I get a reliable PDF of important questions with answers for this chapter?

You can download a free a square and a cube class 8 worksheet PDF or class 8 maths chapter 1 extra questions PDF from Vedantu’s resources. These contain exam-focused questions with stepwise answers, formatted for quick revision and offline practice.

5. What are common mistakes to avoid in “A Square and a Cube” exam questions?

Common errors include:

Forgetting to write steps when finding roots
Misunderstanding between squares and cubes
Ignoring marking keywords
Missing units in answers

Always show your working and highlight final answers clearly.

6. Are diagrams or figures needed in “A Square and a Cube” answers?

Most questions are based on numbers, but some may ask for a figure or pattern to illustrate squares/cubes. Draw diagrams only if asked and label them neat and clear. Including relevant figures helps in visualizing concepts and scoring full marks where applicable.

7. What is the best way to practice exam-focused questions from this chapter quickly?

Use the a square and a cube class 8 sample paper and worksheet sets for fast practice. Time yourself for each section—MCQs, short, and long answers. Mark areas with mistakes, then review class 8 maths chapter 1 a square and a cube question answer notes for quick improvement.