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The units digit of a perfect square is 6. What are the possible values of the tens digit?

 Mar 30, 2019
 #1
avatar+17968 
+2

The squre root has to be a 4 or 6  for the square to end in 6

4         16

6             36

14          196

16        256

24     576

 26       676

34            1156

36           1296

44        1936

46        2116                             So I'd say    1  3  9   5  or   7    for the tens' digit.....

 Mar 31, 2019
 #2
avatar+100008 
+1

squares that end in 6 must be of the form

 

\((10n\pm4)^2\)     where n is an interger 

 

\((10n\pm4)^2\\ =100n^2\pm80n+16\\ =100n^2+10\pm80n+6\\ =100n^2+10(1\pm8n)+6\\ \text{8n can end in any even number so }1\pm8n \text { can end in any odd number}\\ \text{So the 10s place value can have any odd digit.} \)

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 Mar 31, 2019

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