What topics are covered in NCERT Class 10 Maths Chapter 1 Real Numbers?

Chapter 1 Real Numbers covers Euclid's Division Lemma, Fundamental Theorem of Arithmetic, Irrationality of numbers like √2, √3, and decimal expansions of rational numbers.

How many exercises are there in Class 10 Maths Chapter 1?

There are 4 exercises in NCERT Class 10 Maths Chapter 1 Real Numbers: Exercise 1.1 (5 questions), Exercise 1.2 (7 questions), Exercise 1.3 (3 questions), and Exercise 1.4 (3 questions).

Is Euclid's Division Lemma important for the Class 10 board exam?

Yes, Euclid's Division Lemma is very important and commonly tested in Class 10 CBSE board exams. It forms the basis for finding HCF using the division algorithm.

Class 10 · Maths · Chapter 1

Real Numbers — NCERT Solutions

Complete solutions for all 4 exercises. Includes Malayalam explanations.

4 Exercises 18 Questions Malayalam CBSE 2024–25

Chapter Overview: Real Numbers is the first chapter of NCERT Class 10 Mathematics. It introduces students to the Fundamental Theorem of Arithmetic, Euclid's Division Algorithm, the proof of irrationality of numbers like √2 and √3, and decimal representations of rational numbers. This chapter is a foundation for higher mathematics.

Euclid's Division Lemma Fundamental Theorem Irrational Numbers Decimal Expansions

Exercise 1.1

5 Questions · Euclid's Division Lemma

Use Euclid's division algorithm to find the HCF of: (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255

Easy

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5...

Medium

An army contingent of 616 members is to march behind an army band of 32 members...

Easy

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1...

Hard

Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

Hard

Exercise 1.2

7 Questions · Fundamental Theorem of Arithmetic

Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

Easy

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

Easy

Find the LCM and HCF of the following integers by applying the prime factorisation method.

Easy

Given that HCF (306, 657) = 9, find LCM (306, 657).

Easy

Check whether 6ⁿ can end with the digit 0 for any natural number n.

Medium

Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Medium

There is a circular path around a sports field. Sonia takes 18 minutes to drive one round... find the time when they will meet again.

Medium

Exercise 1.3

3 Questions · Irrational Numbers

Prove that √5 is irrational.

Medium

Prove that 3 + 2√5 is irrational.

Medium

Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2

Hard

Exercise 1.4

3 Questions · Decimal Expansions

Without actually performing the long division, state whether the decimal expansion of the following rational numbers will terminate or not.

Easy

Write down the decimal expansions of those rational numbers in Q.1 above which have terminating decimal expansions.

Easy

The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not...

Medium

Frequently Asked Questions

What topics are covered in NCERT Class 10 Maths Chapter 1?

Chapter 1 covers Euclid's Division Lemma, the Fundamental Theorem of Arithmetic (every integer > 1 is either prime or can be expressed as a unique product of primes), proofs that numbers like √2 and √3 are irrational, and terminating vs. non-terminating decimal expansions of rational numbers.

How many exercises are in Chapter 1 Real Numbers?

There are 4 exercises: Exercise 1.1 (5 questions on Euclid's Division Lemma), Exercise 1.2 (7 questions on Fundamental Theorem), Exercise 1.3 (3 questions on Irrationality proofs), and Exercise 1.4 (3 questions on Decimal Expansions) — 18 questions in total.

Is Chapter 1 important for the CBSE Class 10 board exam?

Yes! Real Numbers usually carries 4–6 marks in the CBSE board exam. Euclid's division algorithm, LCM-HCF, and irrationality proofs are frequently asked. Xello tutors focus specifically on board-exam question patterns.

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