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?

Hi6942O Jul 18, 2024

#1**+1 **

If the number 5 is in the units digit, then the original number that was squared must end with 5.

Let's set a variable to help us solve this question.

Let's let **a** be a number that is the multiple of 10. We have

\((a + 5) (a + 5) = \\ a^2 + 10a + 25\)

a^2 will always end with a 0 or two 0s, so it has no effect on the final digit

10a will always end with a 0 or two 0s, so it has no effect on the final digit

This means we always have 25.

So 2 is our answer.

Thanks! :)

NotThatSmart Jul 18, 2024