perfect squares

**perash** · September 15th 2008, 03:26 AM

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.

**Soroban** · September 15th 2008, 11:37 AM

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.

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

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