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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+37167 
0

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+118703 
+1

squares that end in 6 must be of the form

 

(10n±4)2     where n is an interger 

 

(10n±4)2=100n2±80n+16=100n2+10±80n+6=100n2+10(1±8n)+68n can end in any even number so 1±8n can end in any odd numberSo the 10s place value can have any odd digit.

 Mar 31, 2019

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