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

Mastering the visual representation of numbers is simple with our NCERT Solutions for Class 8 Maths Ch 3: A Story of Numbers – Exercise 3.8. This unique exercise moves away from pure calculation and into the world of geometry. You will learn how to construct irrational lengths like $\sqrt{2},\sqrt{3},\text{ and }\sqrt{5}$ on a number line using a compass and ruler, a technique known as the "Square Root Spiral" or "Spiral of Theodorus."

Class 8 Math Lessons (Ch 3): Learn to Draw Square Roots with Ease! The solutions to Exercise 3.8 of Class 8 Maths will be presented in a step-by-step construction approach to give students a clear understanding of how the Pythagoras Theorem forms the basis of all radical lengths. The solutions are in accordance with the CBSE Guidelines to help students excel in practical geometry and internal assessments. Additionally, this exercise serves as a bridge to Class 9 "Number Systems," where representing irrational numbers on a number line is a core topic.

1.0Download Class 8 Maths Chapter 3 Ex 3.7 NCERT Solutions PDF

Our easy-to-follow NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.7 are available for download as a PDF. Perfect for offline study and quick reference before exams.

2.0Key Concepts of Chapter 3 Exercise 3.8

• The Square Root Spiral: A geometric construction where right-angled triangles are built one upon another to create lengths equal to the square roots of consecutive natural numbers.
• Unit Length Construction: Using a fixed unit (e.g., 1 cm or 1 inch) as the base to start the spiral.
• Applying Pythagoras Theorem: Understanding that if the base is $\sqrt{n}$ and the perpendicular is 1, the hypotenuse will be $\sqrt{n+1}$.
• Transferring to Number Line: Using a compass to take the hypotenuse length and "arc" it down onto the horizontal number line.

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

4.0Benefits of NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.8

• Conceptual Clarity: Connects abstract algebra with tangible physical lengths.
• Practical Skills: Improves accuracy with geometry tools like the protractor and compass.
• Logical Steps: Breaks down the "Recursive" nature of the spiral—where the hypotenuse of one triangle becomes the base of the next.
• Error Prevention: Teaches the importance of maintaining a strict 90 degrees angle at each step to ensure the root values are accurate.