Class 10 Exam > Class 10 Questions > Prove that √5 irrational?
Start Learning for Free
Prove that √5 irrational?
Most Upvoted Answer
Prove that √5 irrational?
Proof that √5 is irrational
Step 1: Squaring both sides
Step 2: Rearranging the equation
Step 3: Analyzing the equation
Step 4: Analyzing the equation
Conclusion:
Assumption: √5 is a rational number.
Let √5 be expressed as a fraction in its simplest form, i.e.
√5 = a/b, where a and b are coprime integers (i.e. they have no common factors).
Step 1: Squaring both sides
Squaring both sides of the equation, we get:
5 = a^2/b^2
Step 2: Rearranging the equation
Multiplying both sides by b^2, we get:
5b^2 = a^2
Step 3: Analyzing the equation
Since a^2 is a multiple of 5, we can conclude that a must also be a multiple of 5.
Therefore, we can express a as 5k, where k is an integer.
Substituting this value of a in the equation, we get:
5b^2 = (5k)^2
5b^2 = 25k^2
b^2 = 5k^2
Step 4: Analyzing the equation
Now, we can see that b^2 is a multiple of 5, which means that b must also be a multiple of 5.
However, this contradicts our initial assumption that a and b are coprime.
Therefore, our assumption that √5 is a rational number must be false.
Conclusion:
Thus, we have proved that √5 is an irrational number.
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
|
|
Top Courses for Class 10View all
Prove that √5 irrational?
Question Description
Prove that √5 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 that √5 irrational? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that √5 irrational?.
Prove that √5 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 that √5 irrational? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that √5 irrational?.
Solutions for Prove that √5 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 that √5 irrational? defined & explained in the simplest way possible. Besides giving the explanation of
Prove that √5 irrational?, a detailed solution for Prove that √5 irrational? has been provided alongside types of Prove that √5 irrational? theory, EduRev gives you an
ample number of questions to practice Prove that √5 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