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Some perfect squares (such as 121) have a digit sum (1 + 2 + 1 = 4) that is equal to the square of the digit sum of their square root (\sqrt{121}=11, and (1 + 1)^2 = 4).

 

What is the smallest perfect square greater than 1000 that does not have this property?

 Dec 26, 2021
 #1
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The answer is 1296.

 Dec 26, 2021
 #2
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The 2 smallest I could find that were > 1000 are:

 

10,000 ==1 +  0 + 0 + 0 + 0 ==1

sqrt(10,000) ==100 =[1 + 0 + 0]^2 =1

 

10,201 ==1 + 0 + 2 + 0 + 1 ==4

sqrt(10,201) ==101 ==[1 + 0 + 1]^2 ==4

 Dec 27, 2021

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