• Skip to main content
  • Skip to primary sidebar
  • Skip to footer
  • NCERT Solutions
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • NCERT Exemplar Problems
  • English Grammar
  • MCQ Questions

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3

  • Real Numbers Class 10 Ex 1.1
  • Real Numbers Class 10 Ex 1.2
  • Real Numbers Class 10 Ex 1.3
  • Real Numbers Class 10 Ex 1.4
Board CBSE
Textbook NCERT
Class Class 10
Subject Maths
Chapter Chapter 1
Chapter Name Real Numbers
Exercise Ex 1.3
Number of Questions Solved 3
Category NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3

Ex 1.3 Class 10 Maths Question 1.
Prove that √5 is irrational.
Solution:
Let √5 = \(\frac { p }{ q }\) be a rational number, where p and q are co-primes and q ≠ 0.
Then, √5q = p => 5q2=p2
⇒  p2 – Sq2     … (i)
Since 5 divides p2, so it will divide p also.
Let p = 5r
Then p2 – 25r 2     [Squaring both sides]
⇒ 5q2 = 25r2     [From(i)]
⇒ q2 = 5r2
Since 5 divides q2, so it will divide q also. Thus, 5 is a common factor of both p and q.
This contradicts our assumption that √5 is rational.
Hence, √5 is irrational. Hence, proved.

Ex 1.3 Class 10 Maths Question 2.
Show that 3 + √5 is irrational.
Solution:
Let 3 + 2√5 = \(\frac { p }{ q }\) be a rational number, where p and q are co-prime and q ≠ 0.
Then, 2√5 = \(\frac { p }{ q }\) – 3 = \(\frac { p – 3q }{ q }\)
⇒ √5 =  \(\frac { p – 3q }{ 2q }\)
since  \(\frac { p – 3q }{ 2q }\) is a rational number,
therefore, √5 is a rational number. But, it is a contradiction.
Hence, 3 + √5 is irrational. Hence, proved.

Ex 1.3 Class 10 Maths Question 3.
Prove that the following are irrational.
NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers e2 7
Solution:
(i) Let  \(\frac { 1 }{ \sqrt { 2 } }\) = \(\frac { p }{ q }\) be a rational number,
where p and q are co-prime and q ≠ 0.
Then, √2 = \(\frac { q }{ p }\)
Since \(\frac { q }{ p }\) is rational, therefore, √2 is rational.
But, it is a contradiction that √2 is rational, rather it is irrational.
Hence, \(\frac { 1 }{ \sqrt { 2 } }\) is irrational.
Hence, proved.

(ii) Let 7√5 = \(\frac { p }{ q }\) be a rational number, where p, q are co-primes and q ≠ 0.
Then, √5 = \(\frac { p }{ 7q }\)
Since \(\frac { p }{ 7q }\) is rational therefore, √5 is rational.
But, it is a contradiction that √5 is rational rather it is irrational.
Hence, 7√5 s is irrational.
Hence proved.

(iii) Let 6 + √2 = \(\frac { p }{ q }\) be a rational number, where p, q are co-primes and q ≠ 0.
Then, √2 = \(\frac { p }{ q }\) – 6 = \(\frac { p – 6q }{ q }\)
Since \(\frac { p – 6q }{ q }\) is rational therefore, √2 is rational.
But, it is a contradiction that √2 is rational, rather it is irrational.
Hence, 6 + √2 is irrational.

We hope the NCERT Solutions for Class 10 Mathematics Chapter 1 Real Numbers Ex 1.3 help you. If you have any query regarding NCERT Solutions for Class 10 Mathematics Chapter 1 Real Numbers Ex 1.3, drop a comment below and we will get back to you at the earliest.

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers

Recent Posts

  • MCQ Questions with Answers for Class 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, and 1 all Subjects
  • Angle, Types of Angles
  • AND gate is formed by using two? 1)OR 2)NAND 3)NOT 4)NOR
  • And expression for one minus the quotient of one and a number X?
  • What is average human body temperature in Kelvins?
  • How many moles of caffeine are in a cup, and how many molecules of caffeine?
  • How far will the car have traveled in that time?
  • What is its atomic number?
  • How many neutrons does it have?
  • An atom loses electrons to form what?
  • What is the atomic number of this atom?
  • Which one of these is the answer?
  • What is its concentration?
  • Can an equilateral triangle also be isosceles?
  • What is the charge of an alpha particle?

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
cbse ncert
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions