Prove or disprove that if a and b are rational numbers, then a^b is also rational. ?

NetherCraft 0

4 Answers

  • Proof by counter-example:

    Let a = 3 and b = 1/2, therefore a^b is the square root of 3, which can’t be written as a ratio of two whole numbers, and is therefore irrational.

  • let a = 2 and b = 1/2

    a^b = 2^(1/2) = sqrt(2) which is not a rational number

    Therefore the statement is false

  • Let a=2, b=1/2, both rational.

    a^b = 2^(1/2)= sqrt 2 which is irrational.


  • yes

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