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Prove that 1/3-2√5 is irrational?
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Prove that 1/3-2√5 is irrational?
Proof that 1/3 - 2√5 is irrational
- Assumption: Let us assume that 1/3 - 2√5 is rational.
- Definition: A number is rational if it can be expressed in the form p/q, where p and q are integers and q is not equal to 0.
- Representation: So, let 1/3 - 2√5 = p/q, where p and q are integers and q is not equal to 0.
- Algebraic Manipulation: Multiplying both sides of the equation by q gives us 1/3q - 2√5(q) = p.
- Definition: Since p is an integer, 1/3q must be rational.
- Algebraic Manipulation: Rearranging the equation, we get √5(q) = (p - 1/3q)/2.
- Definition: Since √5 is irrational, (p - 1/3q)/2 must also be irrational.
- Definition: However, the sum or difference of a rational and an irrational number is always irrational.
- Conclusion: This contradicts our assumption that 1/3 - 2√5 is rational. Therefore, 1/3 - 2√5 must be irrational.
Community Answer
Prove that 1/3-2√5 is irrational?
By contradiction method..1st assume that that it's rational..then u will come at wrong statement bcz of incrct assumption....
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Prove that 1/3-2√5 is irrational?
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Prove that 1/3-2√5 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 that 1/3-2√5 is irrational? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that 1/3-2√5 is irrational?.
Prove that 1/3-2√5 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 that 1/3-2√5 is irrational? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that 1/3-2√5 is irrational?.
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