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