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Prove that root 3- root 2 is irrational ?
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Prove that root 3- root 2 is irrational ?
Proof that √3 - √2 is irrational
- Assumption: Let's assume that √3 - √2 is rational
- Definition of Irrational Numbers: An irrational number is a number that cannot be expressed as a ratio of two integers
- Algebraic Manipulation: We can manipulate the equation to get rid of the root sign.
√3 - √2 = x (assume that x is rational)
3 - 2√6 + 2 = x^2
5 - 2√6 = x^2 (since x is rational) - Definition of Square Root: The square root of a number is a value that, when multiplied by itself, gives the number.
x^2 = 5 - 2√6
(x^2 - 5) = -2√6
(x^2 - 5)^2 = 24 - Definition of Even and Odd Numbers: An even number is an integer that is divisible by 2 and an odd number is not divisible by 2.
- Parity: If x is even, then x^2 is even. If x is odd, then x^2 is odd.
- Contradiction: Since (x^2 - 5)^2 is even, 24 must be even. However, 24 is not even which contradicts our assumption that √3 - √2 is rational. Therefore, we can conclude that √3 - √2 is irrational.
Community Answer
Prove that root 3- root 2 is irrational ?
If possible let 3-root 2 be a rational and 3 is rational 3-root 2=rational 3-root 2-3=rational Root 2=rationalIrrational ≠rational This is contradiction which arise due to our wrong supposition Hence 3-root 2 is irrational It's just like a hint.. Hope it will help u
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Prove that root 3- root 2 is irrational ?
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Prove that root 3- root 2 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 2 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 2 is irrational ?.
Prove that root 3- root 2 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 2 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 2 is irrational ?.
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