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Math Help - perfect squares

  1. #1
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    perfect squares

    Find the sum of the square roots of the smallest and largest square numbers (perfect squares) that use each digit (0,1,2,3,4,5,6,7,8,9) once and only once.
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  2. #2
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    Hello, perash!

    Find the sum of the square roots of the smallest and largest square numbers
    (perfect squares) that use each digit (0,1,2,3,4,5,6,7,8,9) once and only once.

    I have no idea how to find such squares, but here's a canonical list.


    . . \begin{array}{ccc} 32043^2 &=& 1,026,753,849 \\<br />
32286^2 &=& 1,042,385,796 \\ 33144^2 &=& 1,098,524, 736 \\<br />
35172^2 &=& 1,237,069,584 \\ 39147^2 &=& 1,532,487,609 \\<br />
\end{array} <br />
\qquad \begin{array}{ccc}45624^2 &=& 2,081,549,376 \\<br />
 55446^2 &=& 3,074,258,916 \\ 68763^2 &=& 4,728,350,169 \\ <br />
83919^2 &=& 7,042,398,561 \\ 99066^2 &=& 9,814,072,356<br />
\end{array}

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