# NCERT Class 10 Mathematics Chapter 1 Real Numbers Solutions: In-Text and Exercise Questions Explained | SwaVid

This document provides a comprehensive set of questions and detailed, step-by-step solutions for Chapter 1, "Real Numbers," from the NCERT Class 10 Math...

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# Real Numbers

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Chapter 1 · Class 10 Mathematics

This document provides a comprehensive set of questions and detailed, step-by-step solutions for Chapter 1, "Real Numbers," from the NCERT Class 10 Mathematics textbook. The content covers all exercises within the chapter, including problems based on Euclid's Division Lemma, the Fundamental Theorem of Arithmetic, proving the irrationality of numbers, and exploring terminating and non-terminating decimal expansions of rational numbers. Each solution is designed to be clear and easy for Class 10 students to follow, reinforcing key mathematical concepts.

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Exercise 1.1

Answer: The HCF of 135 and 225 is 45.

Exercise 1.2

Exercise 1.3

Exercise 1.4

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- Apply Euclid's division lemma to 225 and 135. Since 225 > 135, we write 225 = 135 × 1 + 90.
- Since the remainder 90 ≠ 0, apply Euclid's division lemma to the divisor 135 and remainder 90. We write 135 = 90 × 1 + 45.
- Since the remainder 45 ≠ 0, apply Euclid's division lemma to the divisor 90 and remainder 45. We write 90 = 45 × 2 + 0.
- The remainder is now 0. The divisor at this stage is 45. Therefore, the HCF of 135 and 225 is 45.
- NCERT Class 10 Mathematics textbook: Mathematics : Chapter 1: Real Numbers

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