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Math Help - Sum of Square Roots...

  1. #1
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    Sum of Square Roots...

    Although 2^(1/2) + 3^(1/2) does not equal the square root of an integer, 27^(1/2) + 48^(1/2) does. Find every set of different positive integers p, q, and r all less than 100 such that p and q are not perfect squares and p^(1/2) + q^(1/2) = r^(1/2).
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  2. #2
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    Re: Sum of Square Roots...

    Quote Originally Posted by thamathkid1729 View Post
    Although 2^(1/2) + 3^(1/2) does not equal the square root of an integer, 27^(1/2) + 48^(1/2) does. Find every set of different positive integers p, q, and r all less than 100 such that p and q are not perfect squares and p^(1/2) + q^(1/2) = r^(1/2).
    Here is a start but a solution without restrictions.
    If p=a^{2m+1}~\&~q=b^{2n}\cdot a where \{a,b,m,n\}\subset \mathbb{Z}^+ will work.
    Now you must impose the restrictions.
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  3. #3
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    Re: Sum of Square Roots...

    wouldn't p = c^{2n}a, q = b^{2n}a work as well?
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  4. #4
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    Re: Sum of Square Roots...

    Quote Originally Posted by Deveno View Post
    wouldn't p = c^{2n}a, q = b^{2n}a work as well?
    Well of course it would.
    I did say that was only a starting point.
    We need to let the poster discover cases for him/her self.
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  5. #5
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    Re: Sum of Square Roots...

    oops, my bad...don't spank me, ok?
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