NCERT Solutions Class 10 Maths Chapter 1 – Real Numbers Exercise 1.3 are provided here to assist students with Class 10 exam preparations. These solutions are carefully prepared by subject experts to help students understand the divisibility rules, Euclid's Division Algorithm, and applications to find the greatest common divisor (gcd) in a step-by-step manner.
Exercise 1.3 in Real Numbers focuses on solving problems related to Euclid’s Division Algorithm and applying it to find the gcd of two numbers. The solutions cover important concepts such as dividing integers, finding the remainder, and using the algorithm to compute gcd, which are crucial for mastering number theory.
NCERT Solutions for Class 10 Maths Chapter 1 – Real Number Exercise 1.3
Q.
Which of the following is a rational number between
3 and 5?
[CBSE - 2025]
Q.
Prove that
51 is an irrational number.
[CBSE - 2025]
Q.
Prove that
5 – 23 is an irrational number. It is given that
3 is an irrational number.
[CBSE - 2024]
NCERT Solutions for Class 10 Maths Chapter 1 – Real Number Exercise 1.3
These solutions are aligned with the latest CBSE syllabus, providing step-by-step explanations and detailed solutions that will help students prepare effectively for their exams and understand the applications of Euclid's Division Algorithm in various types of problems.
Question:
Which of the following is a rational number between and ?
Answer:
There is no rational number between and as both of these are irrational numbers and the numbers between them are also irrational.
Question:
Prove that is an irrational number.
Answer:
To prove that is irrational, assume the opposite that it is rational. Hence, for some integers and such that and are coprime. Squaring both sides gives , which results in a contradiction, as 5 cannot be the square of a rational number. Therefore, is irrational.
Question:
Prove that is an irrational number. It is given that is irrational.
Answer:
Suppose is rational. Then, must be rational, which contradicts the fact that is irrational. Hence, is irrational.
FAQs: Class 10 Maths Chapter 1 – Real Numbers Exercise 1.3
Q1. What is the main concept covered in Exercise 1.3?
Answer:
Exercise 1.3 focuses on finding the greatest common divisor (gcd) of two numbers using Euclid's Division Algorithm and solving related division and remainder problems.
Q2. How do I apply Euclid's Division Algorithm in Exercise 1.3?
Answer:
To apply Euclid's Division Algorithm, divide the number a by b and express it as:
a = b × q + r,
where a is the dividend, b is the divisor, q is the quotient, and r is the remainder. Continue applying the algorithm until the remainder is 0, and the divisor at that step will be the gcd.
Q3. What is the significance of finding the gcd using Euclid's Division Algorithm?
Answer:
Finding the gcd of two numbers helps in simplifying fractions, finding lcm, and solving problems related to number theory. It is also used in cryptography, data compression, and error detection algorithms.
Q4. Are there any tips for solving problems in Exercise 1.3?
Answer:
-
Make sure you correctly identify the dividend and divisor in each problem.
-
Always perform division step by step and carefully subtract the remainder.
-
Remember that the gcd is the last non-zero remainder.
Q5. How do NCERT Solutions help with exam preparation?
Answer:
These solutions provide clear, logical explanations and step-by-step solutions to the problems, making it easier for students to understand Euclid’s Division Algorithm and apply it effectively in exams. Practicing these solutions helps in building confidence and scoring well in exams.