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How to prove an irrational number? Video Lecture | Mathematics (Maths) Class 10
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FAQs on How to prove an irrational number? Video Lecture - Mathematics (Maths) Class 10
| 1. How do you prove that a number is irrational? |  |
Ans. To prove that a number is irrational, one can use proof by contradiction or proof by contradiction method. In proof by contradiction, we assume that the number is rational and then derive a contradiction. This contradiction proves that the number cannot be rational and hence it must be irrational.
| 2. What is the proof by contradiction method? | |
Ans. Proof by contradiction is a method of proving a statement by assuming the opposite and showing that it leads to a contradiction. In the context of proving an irrational number, we assume that the number is rational and express it as a fraction p/q, where p and q are integers with no common factors. By manipulating the equation, we arrive at a contradiction that shows our assumption was incorrect, proving that the number is irrational.
| 3. Can all irrational numbers be proved using the proof by contradiction method? | |
Ans. No, not all irrational numbers can be proved using the proof by contradiction method. While the proof by contradiction is a commonly used method, there are other techniques as well, such as the decimal representation method or the continued fraction method. The choice of proof method depends on the specific irrational number being considered.
| 4. What are some examples of irrational numbers that can be proved using the proof by contradiction method? | |
Ans. Examples of irrational numbers that can be proved using the proof by contradiction method include √2, e (Euler's number), and π (pi). By assuming that these numbers are rational and following the proof by contradiction method, we can show that they cannot be expressed as fractions and are therefore irrational.
| 5. Are all irrational numbers difficult to prove? | |
Ans. Not all irrational numbers are difficult to prove. While some irrational numbers require more complex proof techniques, such as the square root of prime numbers, there are also irrational numbers that can be easily proved using basic mathematical concepts. It depends on the specific irrational number and the proof method chosen.
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Dec 23, 2024 Last updated |
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