Students should revise definitions, practise all NCERT exercises, and solve important questions based on HCF, LCM, and divisibility. Repeated practice of stepwise solutions helps build accuracy and confidence for exams.

Q: How is prime factorization related to HCF and LCM?

Prime factorisation helps us break numbers into prime factors, which makes it easier to find the HCF and LCM by comparing common and all prime factors.

Q: How do we prove that a number is irrational?

A number is proved to be irrational by the method of contradiction. First, assume it is rational. Then simplify the expression using the properties of rational numbers. If this leads to a contradiction with a known fact, the assumption is false. Hence, the number is irrational.

Access Answers to NCERT Solutions for Class 10 Maths Chapter 1: Real Numbers

Students can access the NCERT Solutions for Class 10 Maths Chapter 1: Real Numbers. Curated by experts according to the CBSE syllabus for 2025–2026, these step-by-step solutions make Maths much easier to understand and learn for the students. These solutions can be used in practice by students to attain skills in solving problems, reinforce important learning objectives, and be well-prepared for tests.

Frequently Asked Questions of NCERT Solutions Class 10 Maths Chapter 1 Real Numbers

1. What is the main concept of Class 10 Maths Chapter 1 Real Numbers?

Chapter 1 focuses on understanding real numbers, including rational and irrational numbers, Euclid’s Division Lemma, and the Fundamental Theorem of Arithmetic. These ideas are used to solve HCF-LCM and factorisation-based problems.

2. What is Euclid’s Division Lemma?

Euclid’s Division Lemma says that for any two positive integers a and b, there exist unique integers q and r such that 𝑎 = 𝑏𝑞 + 𝑟 where 0 ≤ r < b.

3. How should students prepare Chapter 1 Real Numbers effectively?

Students should revise definitions, practise all NCERT exercises, and solve important questions based on HCF, LCM, and divisibility. Repeated practice of stepwise solutions helps build accuracy and confidence for exams.

4. How is prime factorization related to HCF and LCM?

Prime factorisation helps us break numbers into prime factors, which makes it easier to find the HCF and LCM by comparing common and all prime factors.

5. How do we prove that a number is irrational?

A number is proved to be irrational by the method of contradiction. First, assume it is rational. Then simplify the expression using the properties of rational numbers. If this leads to a contradiction with a known fact, the assumption is false. Hence, the number is irrational.

Next Chapter

Admissions Open for 2026-27