BSEB Class 10 Maths Chapter 1 Real Numbers Ex 1.3 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 1 Real Numbers Ex 1.3 Book Answers ~ HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

BSEB Class 10 Maths Chapter 1 Real Numbers Ex 1.3 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 1 Real Numbers Ex 1.3 Book Answers

BSEB Class 10th Maths Chapter 1 Real Numbers Ex 1.3 Textbooks Solutions and answers for students are now available in pdf format. Bihar Board Class 10th Maths Chapter 1 Real Numbers Ex 1.3 Book answers and solutions are one of the most important study materials for any student. The Bihar Board Class 10th Maths Chapter 1 Real Numbers Ex 1.3 books are published by the Bihar Board Publishers. These Bihar Board Class 10th Maths Chapter 1 Real Numbers Ex 1.3 textbooks are prepared by a group of expert faculty members. Students can download these BSEB STD 10th Maths Chapter 1 Real Numbers Ex 1.3 book solutions pdf online from this page.

Bihar Board Class 10th Maths Chapter 1 Real Numbers Ex 1.3 Textbooks Solutions PDF

Bihar Board STD 10th Maths Chapter 1 Real Numbers Ex 1.3 Books Solutions with Answers are prepared and published by the Bihar Board Publishers. It is an autonomous organization to advise and assist qualitative improvements in school education. If you are in search of BSEB Class 10th Maths Chapter 1 Real Numbers Ex 1.3 Books Answers Solutions, then you are in the right place. Here is a complete hub of Bihar Board Class 10th Maths Chapter 1 Real Numbers Ex 1.3 solutions that are available here for free PDF downloads to help students for their adequate preparation. You can find all the subjects of Bihar Board STD 10th Maths Chapter 1 Real Numbers Ex 1.3 Textbooks. These Bihar Board Class 10th Maths Chapter 1 Real Numbers Ex 1.3 Textbooks Solutions English PDF will be helpful for effective education, and a maximum number of questions in exams are chosen from Bihar Board.

Bihar Board Class 10th Maths Chapter 1 Real Numbers Ex 1.3 Books Solutions

Board	BSEB
Materials	Textbook Solutions/Guide
Format	DOC/PDF
Class	10th
Subject	Maths Chapter 1 Real Numbers Ex 1.3
Chapters	All
Provider	Hsslive

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BSEB Bihar Board Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.3

Question 1.
Prove that 5‾√ is irrational. [CBSE, Delhi 2009]
Solution:
Let us assume, to the contrary, that 5‾√ is rational.
Squaring on both sides, we get
5 = 𝑎2𝑏2 or 5b² = a² ………………. (1)
This shows that a² is divisible by 5.
It follows that a is divisible by 5. …………………. (2)
So, a = 5m for some integer m.
Substituting a = 5m in (1), we get
5b² = (5m)² = 25m²
or b² = 5m² or b² is divisible by 5
and hence b is divisible by 5.
From (2) and (3), we can conclude that 5 is a common factor of both a and b.
But this contradicts our supposition that a and b are coprime.
Hence, 5‾√ is irrational.

Question 2.
Prove that 3 + 25‾√ is irrational.
Solution:
Let us assume, to the contrary, that 3 + 25‾√ is a rational number.
Now, let 3 + 25‾√ = 𝑎𝑏, where a and b are coprime and b ≠ 0.
So, 25‾√ = 𝑎𝑏 – 3 or 5‾√ = 𝑎2𝑏 – 32
Since a and b are integers, therefore
𝑎2𝑏 – 32 is a rational number.
∴ 5‾√ is an irrational number.
But 5‾√ is an irrational number.
This shows that our assumption is incorrect.
So, 3 + 25‾√ is an irrational number.

Question 3.
Prove that the following are irrationals:

12√
75‾√
6 + 2‾√

Solution:
1. Let us assume, to the contrary, that 12√ is rational.
That is, we can find co-prime integers p and q (≠ 0) such that

Since p and q are integers, 2𝑝𝑞 is rational, and so 2‾√ is rational.
But this contradicts the fact that 2‾√ is irrational.
So, we conclude that 12√ is irrational.

2. Let us assume, to the contrary, that 75‾√ is rational.
That is, we can find co-prime integers p and q (≠ 0) such that 75‾√ = 𝑝𝑞.
So, 5‾√ = 𝑝7𝑞.
Since p and q are integers, 𝑝7𝑞 is rational and so is 5‾√.
But this contradicts the fact that 5‾√ is irrational.
So, we conclude that 75‾√ is irrational.

3. Let us assume, to the contrary, that 6 + 2‾√ is rational.
That is, we can find integers p and q (≠ 0) such that
6 + 2‾√ = 𝑝𝑞 or 6 – 𝑝𝑞 = 2‾√
or 2‾√ = 6 – 𝑝𝑞
Since p and q are integers, we get 6 – 𝑝𝑞 is rational, and so 2‾√ is rational.
But this contradicts the fact that 2‾√ is irrational.
So, we conclude that 6 + 2‾√ is irrational.

BSEB Textbook Solutions PDF for Class 10th

Bihar Board Class 10th Maths Chapter 1 Real Numbers Ex 1.3 Textbooks for Exam Preparations

Bihar Board Class 10th Maths Chapter 1 Real Numbers Ex 1.3 Textbook Solutions can be of great help in your Bihar Board Class 10th Maths Chapter 1 Real Numbers Ex 1.3 exam preparation. The BSEB STD 10th Maths Chapter 1 Real Numbers Ex 1.3 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 10th Maths Chapter 1 Real Numbers Ex 1.3 Books State Board syllabus with maximum efficiency.

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