Question about determining digits of a number

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To solve the equation \(\sqrt{ABADEC} = BEB\), one approach is to express BEB in terms of its digits, resulting in the equation \(BEB = 101B + 10E\). Squaring this expression will yield \(ABADEC\), which can then be analyzed to find the digit "D." Participants suggest focusing on the relationship between the digits and the structure of the numbers involved. The discussion emphasizes the importance of manipulating the squared expression to derive further insights into the value of "D."
GeoMike
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The question is:
If \sqrt{ABADEC} = BEB what is the value of the digit "D"?

I'm completely lost as to how to start on this one. I tried expanding the numbers as powers of ten:
BEB = B*102 + E*101 + B*100
= B(102 + 1) + 10E
= 101B + 10E
...but I couldn't really do anything with it after that.

I don't want an answer, just a hint on how to proceed.

Thanks!
-GM-
 
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GeoMike said:
BEB = B*102 + E*101 + B*100

Try taking this expression and squaring it.
 
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