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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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