Class 10 Exam > Class 10 Videos > 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths
05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths Video Lecture
FAQs on 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths Video Lecture
| 1. What are irrational numbers? |  |
Ans. Irrational numbers are real numbers that cannot be expressed as a ratio or fraction of two integers. They are non-repeating and non-terminating decimals. Examples of irrational numbers include √2, π, and e.
| 2. How can we prove that √2 is irrational? | |
Ans. The proof of √2 being irrational is a classic mathematical proof. It involves assuming that √2 is rational and then arriving at a contradiction. The proof shows that if √2 is rational, then it can be expressed as a fraction of two integers. However, by simplifying this assumed fraction, we find that the numerator and denominator have a common factor of 2, which contradicts the assumption that the fraction is in its simplest form. Therefore, √2 is irrational.
| 3. Are all square roots irrational numbers? | |
Ans. No, not all square roots are irrational numbers. Square roots of perfect squares (numbers that are the square of an integer) are rational numbers. For example, the square root of 25 is 5, which is a rational number. However, square roots of non-perfect squares, such as √2 and √7, are irrational numbers.
| 4. Can irrational numbers be expressed as decimals? | |
Ans. Yes, irrational numbers can be expressed as decimals. However, unlike rational numbers, which either terminate or repeat, irrational numbers have non-repeating and non-terminating decimal representations. For example, the decimal representation of √2 is approximately 1.41421356, and it continues indefinitely without repeating any pattern.
| 5. Are all numbers that cannot be expressed as fractions irrational? | |
Ans. No, not all numbers that cannot be expressed as fractions are irrational. Some numbers that cannot be expressed as fractions are transcendental numbers, such as π and e. Transcendental numbers are real numbers that are not algebraic, meaning they are not the root of any non-zero polynomial equation with integer coefficients. Therefore, while all irrational numbers cannot be expressed as fractions, not all numbers that cannot be expressed as fractions are irrational.
Related Exams
About this Video
|
4.78/5 Rating |
|
Dec 23, 2024 Last updated |
05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths for Class 102024 is part of Class 10 preparation. The notes and questions for 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths
have been prepared according to the Class 10 exam syllabus. Information about 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths covers all important topics
for Class 102024 Exam. Find important definitions, questions, notes, meanings, examples, exercises
and tests below for 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths.
Introduction of 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths in English is available as part of our Class 10 preparation & 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths in Hindi
for Class 10 courses. Download more important topics, notes, lectures and mock test series for Class 10 Exam by
signing up for free.
Description
Video Lecture & Questions for 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths Video Lecture - Class 10 full syllabus preparation | Free video for Class 10 exam.
Information about 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths
Here you can find the 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths defined & explained in the simplest way possible. Besides explaining types of 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths
theory, EduRev gives you an ample number of questions to practice 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths tests, examples and also practice Class 10 tests.
|
Explore Courses for Class 10 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Previous Year Questions with Solutions
,past year papers
,practice quizzes
,Extra Questions
,MCQs
,Free
,ppt
,Semester Notes
,study material
,Viva Questions
,05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths Video Lecture
,mock tests for examination
,Objective type Questions
,Sample Paper
,Exam
,Summary
,shortcuts and tricks
,05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths Video Lecture
,video lectures
,Important questions
,05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths Video Lecture
;
Study 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths on the App
Students of Class 10 can study 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of 05 - Irrational Numbers And Proof Of Root 2 Is Irrational - Class 10 - Maths is prepared as per the latest Class 10 syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup