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Prove that root 3+ root 7 is irrational?
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Prove that root 3+ root 7 is irrational?
Proof that √3 + √7 is irrational:
- Assume √3 + √7 is rational
- Let's assume √3 + √7 = a/b, where a and b are integers with no common factors
- Squaring both sides, we get 3 + 2√21 + 7 = a^2/b^2
- Which simplifies to 2√21 = a^2/b^2 - 10
- Since √21 is irrational, a and b must cancel out, leading to a contradiction
- Therefore, our initial assumption that √3 + √7 is rational is false
- Hence, √3 + √7 is irrational
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Prove that root 3+ root 7 is irrational?
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Prove that root 3+ root 7 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 root 3+ root 7 is irrational? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that root 3+ root 7 is irrational?.
Prove that root 3+ root 7 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 root 3+ root 7 is irrational? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that root 3+ root 7 is irrational?.
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