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maths- rational no.

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find two irrational numbers between 2.5 and 4.5

  • maths- rational no. - ,

    2.5 = 5/2
    4.5 = 9/2

    so, a short list of rational numbers between the two might contain

    6/2 7/2 8/2

    Expressing them as 6ths,
    2.5 = 15/6
    4.5 = 27/6
    Now there are a lot more possibilities, all multiples of 1/6

  • maths- rational no. - ,

    Oops! I missed the "irrational" part!

    Since
    2.5^2 = 6.25
    4.5^2 = 20.25

    Pick any integers between those, except 9 and 16, which are perfect squares.

    √7 √8 √10 ... √20
    are all irrational.

    Since
    2.5^3 = 15.625
    4.5^3 = 91.125

    There are lots of possibilities there, excluding 27 and 64:

    ∛16 ∛17 ... ∛91
    are all irrational

    You can pick non-integer values, as long as they don't turn out to be perfect powers.

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