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NCERT Solutions
Class 8
Maths
Chapter 3 A Story of Numbers
Exercise 3.4

Frequently Asked Questions

Prime factorization becomes very difficult if the number has large prime factors (like 97). The Long Division method doesn't care about the prime factors; it only cares about the digits, making it much faster.

For the whole number part, go from right to left. For the decimal part, go from left to right.

Find the square root by division. You will get a remainder. The number's root lies between your current quotient (q) and the next number (q+1). The number to add is (q+1)^2 - Original Number.

Yes. You can add pairs of zeros after the decimal point and continue the process to find the square root up to any number of decimal places.

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NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers - Exercise 3.4

Mastering the calculation of square roots for large numbers and decimals is simple with our NCERT Solutions for Class 8 Maths Ch 3: A Story of Numbers – Exercise 3.4. While prime factorization is effective for smaller numbers, it becomes tedious for larger ones. Exercise 3.4 introduces the Long Division Method, a systematic algorithm that works efficiently for any number, including those that are not perfect squares.

Class 8 Math Lessons (Ch 3): Learn to Find Square Roots of Large Numbers with Ease! The NCERT Solutions to Exercise 3.4 of Class 8 Maths will be presented in a step-by-step approach so as to give students a good understanding of how to group digits and estimate divisors. The solutions are in accordance with the CBSE Guidelines so as to provide students with the best path available to improve their speed and accuracy in long-form calculations. Additionally, these solutions will aid students in building a solid foundation for competitive exams and higher-level physics/chemistry calculations.

1.0Download NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers Ex 3.4 : PDF

Our easy-to-follow NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.4 are available for download as a PDF. Perfect for offline study and quick reference before exams.

NCERT Solutions Class 8 Maths Chapter 3 Ex 3.4

Download PDF

2.0Key Concepts of Chapter 3 Exercise 3.4

  • The Division Algorithm: A systematic way to find square roots by placing bars over pairs of digits.
  • Grouping (Bars): Placing bars over pairs of digits starting from the unit's place. If the total number of digits is odd, the leftmost digit will have a single bar.
  • Square Roots of Decimals: Applying the division method to decimals by pairing digits to the left and right of the decimal point.
  • Finding the Least Number to Subtract: Determining what remainder is left when a number is not a perfect square, indicating how much must be removed to make it one.
  • Finding the Least Number to Add: Calculating how much more is needed to reach the next perfect square.

3.0NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers : All Exercises

NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers - Exercise 3.1

NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers - Exercise 3.2

NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers - Exercise 3.3

NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers - Exercise 3.4

NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers - Exercise 3.5

NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers - Exercise 3.6

NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers - Exercise 3.7

NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers - Exercise 3.8

NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers - Exercise 3.9

4.0Benefits of NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.4

  • Conceptual Clarity: Detailed breakdown of the "doubling the quotient" rule which is often the hardest part for students.
  • Exam-Oriented: Focuses on the "least number to add/subtract" questions, which are high-scoring and very common.
  • Logical Steps: Each step of the division is explained to ensure students understand why a specific digit is chosen.
  • Error Prevention: Highlights common mistakes in decimal pairing (e.g., pairing from the decimal point outward).

NCERT Class 8 Maths Ch. 3 A Story of Numbers Other Exercises:-

Exercise 3.1

Exercise 3.2

Exercise 3.3

Exercise 3.4

Exercise 3.5

Exercise 3.6

Exercise 3.7

Exercise 3.8

Exercise 3.9


NCERT Solutions Class 8 Maths All Chapters:-

Chapter 1 - A Square and a Cube

Chapter 2 - Power play

Chapter 3 - A story of Numbers

Chapter 4 - Quadrilaterals

Chapter 5 - Number Play

Chapter 6 - We distibute, yet thinmgs multiply

Chapter 7 - Proportional Reasoning