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The numbers $24^2 = 576$ and $56^2 = 3136$ are examples of perfect squares that have a units digits of $6.$
If the units digit of a perfect square is $5,$ then what are the possible values of the tens digit?

 Jul 7, 2024
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The numbers $24^2 = 576$ and $56^2 = 3136$ are examples of perfect squares that have a units digits of $6.$   
If the units digit of a perfect square is $5,$ then what are the possible values of the tens digit?
   

 

If a number ends with 5, its square will end with 25.  

So the only possible value of the tens digit is 2.   

 

How to square a number that ends with a 5.   

Separate the 5 out of the number.  

Change that 5 to 25.   

Add 1 to the number that is left. 

Multiply that by the original number.   

Stick the 25 to the end of the product.   

 

Examples:  

 

   152                              452                              752                              1252       

   1                  5              4                  5             7                  5              12                  5   

   1                25              4                25             7                25              12                25    

   1 x (1+1)    25              4 x (4+1)    25             7 x (7+1)    25              12 x (12+1)  25    

   1 x 2           25              4 x 5          25             7 x 8           25              12 x 13        25     

   225                              2025                           5625                             15625          

.

 Jul 7, 2024

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