irrational numbers?!

what are rational and irrational numbers??
i know that irrational numbers are numbers that cannot be expressed as a fraction, but i'm still confused.

there is this question:

which of the following are irrational numbers: √2, √8, 22/7, pi, 2√3

i know that 22/7 is rational, pi is irrational, but what about those square roots?

asked by Sanchia
  1. Square roots of numbers that are not the squares of integers are all irrational. There is a way to prove that but I forgot the details. You have to assume that a fraction works and then prove that the assumption leads to a contradiction

    Any number that does not meet the definition of being rational is irrational.

    posted by drwls
  2. - √2 is either rational or irrational.

    - Assume that √ is rational so that
    √2 = a/b, with a/b in lowest terms
    - Square both sides to get
    2 = a^2/b^2
    then a^2 = 2b^2
    - the right side of this equation is clearly an even number, since anything multiplied by 2 is even
    - so a^2 must be even. We also know that if we square an odd number the result is odd, and if we square an even number the result is even
    so a must be even
    so a could be written as 2k
    - rewriting our equation as
    2b^2= (2k)^2
    2b^2 = 4k^2
    b^2 = 2k^2

    by the same argument as above 2k^2 is even , so b has to be even

    which means a and b are both even, therefore a/b is not in lowest terms

    BUT that contradicts my assumption that a/b was a fraction in lowest terms

    so √2 = a/b is a false statement
    therefore √2 cannot be rational, and
    must then be irrational

    the same argument could be used for √3 and all other square roots

    posted by Reiny
  3. true or false does this number represent a rational number 0.20200200020000200000

    posted by brandy
  4. Is √4 Irrational?

    posted by Amber
  5. is this seriouly the answer for the LEAP test *feecepum*
    you're not going to get ALL 50 answers -_-

    posted by Cereal.... is life. -Life Cereal

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