Class 10 Exam > Class 10 Questions > Prove under root 1÷2 is irrational?
Start Learning for Free
Prove under root 1÷2 is irrational?
Most Upvoted Answer
Prove under root 1÷2 is irrational?
To prove 1/√2 is irrational
Let us assume that √2 is irrational
1/√2 = p/q (where p and q are co prime)
q/p = √2
q = √2p
squaring both sides
q² = 2p² (1)
By theorem
q is divisible by 2
∴ q = 2c ( where c is an integer)
putting the value of q in equitation 1
2p² = q² = 2c² =4c²
p² =4c² /2 = 2c²
p²/2 = c²
by theorem p is also divisible by 2
But p and q are coprime
This is a contradiction which has arisen due to our wrong assumption
∴1/√2 is irrational.
Let us assume that √2 is irrational
1/√2 = p/q (where p and q are co prime)
q/p = √2
q = √2p
squaring both sides
q² = 2p² (1)
By theorem
q is divisible by 2
∴ q = 2c ( where c is an integer)
putting the value of q in equitation 1
2p² = q² = 2c² =4c²
p² =4c² /2 = 2c²
p²/2 = c²
by theorem p is also divisible by 2
But p and q are coprime
This is a contradiction which has arisen due to our wrong assumption
∴1/√2 is irrational.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
Prove under root 1÷2 is irrational?
Question Description
Prove under root 1÷2 is irrational? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Prove under root 1÷2 is irrational? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove under root 1÷2 is irrational?.
Prove under root 1÷2 is irrational? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Prove under root 1÷2 is irrational? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove under root 1÷2 is irrational?.
Solutions for Prove under root 1÷2 is irrational? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Prove under root 1÷2 is irrational? defined & explained in the simplest way possible. Besides giving the explanation of
Prove under root 1÷2 is irrational?, a detailed solution for Prove under root 1÷2 is irrational? has been provided alongside types of Prove under root 1÷2 is irrational? theory, EduRev gives you an
ample number of questions to practice Prove under root 1÷2 is irrational? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup