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Proving given number as Irrational Video Lecture - Class 10
FAQs on Proving given number as Irrational Video Lecture - Class 10
| 1. What is an irrational number? |  |
Ans. An irrational number is a real number that cannot be expressed as a fraction or ratio of two integers. It is a number that goes on infinitely without repeating and cannot be written as a terminating or repeating decimal.
| 2. How can we prove a number as irrational? | |
Ans. To prove a number as irrational, we can use various methods such as proof by contradiction, proof by infinite descent, or proof by uniqueness. These methods involve logical reasoning and mathematical techniques to show that the given number cannot be expressed as a rational number.
| 3. Can you provide an example of an irrational number? | |
Ans. Yes, one of the most well-known examples of an irrational number is the square root of 2 (√2). It cannot be expressed as a fraction or ratio of two integers, and its decimal representation goes on infinitely without repeating.
| 4. Is it possible for a number to be both rational and irrational? | |
Ans. No, a number cannot be both rational and irrational. A number can only fall into one category. If a number can be expressed as a fraction or ratio of two integers, it is rational. If it cannot be expressed in such a way and goes on infinitely without repeating, it is irrational.
| 5. Why is proving a number as irrational important in mathematics? | |
Ans. Proving a number as irrational is important in mathematics as it helps classify numbers and understand their properties. It allows us to distinguish between rational and irrational numbers, which have different characteristics and behave differently in mathematical operations. Additionally, proving a number as irrational often involves the use of rigorous logical reasoning, which is a fundamental skill in mathematics.
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Nov 16, 2024 Last updated |
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