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Math Help - Perfect Square Probability

  1. #1
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    Perfect Square Probability

    An integer n is randomly chosen from 1 to k^2, where k is an integer. What is the probability that n is a perfect square?

    I have determined that the probability of n being a perfect square is 1/k?

    If I am correct above, does this imlpy that the probability of n^(1/2) being irrational is (k-1)/k?
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  2. #2
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    Re: Perfect Square Probability

    Quote Originally Posted by thamathkid1729 View Post
    An integer n is randomly chosen from 1 to k^2, where k is an integer. What is the probability that n is a perfect square?
    I have determined that the probability of n being a perfect square is 1/k?
    If I am correct above, does this imlpy that the probability of n^(1/2) being irrational is (k-1)/k?
    It is well known that if the \sqrt{n} is rational the n is a square.

    If k\in\mathbb{Z}^+ and n\in[1,k^2]\cap\mathbb{Z}^+ is random then the probability that \sqrt{n} is rational is \frac{1}{k}.
    Is that your question?
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  3. #3
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    Re: Perfect Square Probability

    Basically, yes
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