Welcome to the ultimate guide on CBSE Class 10 Maths Chapter 1 – Real Numbers Solutions. If you're a Class 10 student preparing for board exams or revising the Real Numbers chapter, this blog will help you learn every concept clearly, with exercise-wise video solutions provided to enhance your understanding.
Keywords: Real Numbers Class 10, CBSE Maths Chapter 1 Solutions, NCERT Exercise 1.1 to 1.4, Class 10 Maths Video Solutions
Semantic Keywords: Euclid's Division Lemma, Fundamental Theorem of Arithmetic, HCF and LCM, Irrational Numbers, Decimal Expansions, Terminating and Non-Terminating Numbers
Exercise-Wise Video Solutions – Class 10 Real Numbers
To make your preparation smoother, here are direct links to detailed video explanations for each exercise of Chapter 1. These are designed to help you understand concepts, solve questions, and revise effectively.
1. Introduction to Real Numbers – Class 10 Maths
Real Numbers include natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Chapter 1 of Class 10 CBSE Maths deepens your understanding of this number system, and introduces you to mathematical logic and proofs.
You’ll explore:
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Euclid’s Division Lemma
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Fundamental Theorem of Arithmetic
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Irrational Numbers
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Rational Numbers and Decimal Expansions
This chapter is not just for your board exams but also builds a base for future topics in mathematics and competitive exams.
2. Key Concepts Explained – Real Numbers Class 10
a) Euclid’s Division Lemma
Used to find HCF of two numbers using the formula:
a = bq + r, where 0 ≤ r < b
b) Fundamental Theorem of Arithmetic
Every composite number has a unique prime factorisation, ignoring the order of factors.
c) Proofs of Irrational Numbers
Use the method of contradiction to prove that √2, √3, etc., are irrational.
d) Rational Numbers & Decimal Expansions
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Terminating decimals: Only 2 and/or 5 in denominator after simplification
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Non-terminating repeating decimals: Other prime factors in denominator
3. Real-Life Applications of Real Numbers
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Banking: Use of decimal expansions in interest calculations
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Engineering: Prime numbers and irrational numbers in measurements
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Programming: Encryption algorithms based on prime factorisation
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Music & Design: HCF/LCM concepts in beat synchronization and pattern design
4. Tips to Master Chapter 1 – Real Numbers
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Learn prime numbers up to 100
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Understand rather than memorize theorems
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Practice proofs logically
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Use video solutions to revise difficult parts
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Attempt NCERT Exemplar and sample paper questions
5. FAQs – Real Numbers Class 10
Q: How many marks is Chapter 1 usually worth?
A: Generally, it carries 6 marks, but its concepts are useful throughout the syllabus.
Q: Is Euclid’s Lemma important for boards?
A: Yes, often asked as direct questions or used in other problems.
Q: Can video solutions replace books?
A: No, but they complement your textbook by providing step-by-step guidance.
6. Final Words – Build Your Foundation Strong
Class 10 Chapter 1 – Real Numbers may look simple but is a core chapter for building mathematical thinking. With clear concepts and consistent practice, you’ll not only ace your board exams but also become strong in fundamentals used in algebra, geometry, and number theory.
Use the video links, bookmark this blog, and keep revising!
If you liked this blog, share it with your classmates. More chapters and video solutions coming soon.
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