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# number theory help this quesiton is due soon

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

HINT: Let our perfect square be n^2. What can the units digit of  be?

Aug 20, 2020

#1
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The possible values of the tens digit are 1, 2, 4, 5, and 6.

Aug 20, 2020
#3
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The only numbers that can be squared to end in 6 are numbers that end in 4 or 6.

We need to find the possible values of the tens digit, so lets let the tens digit be a variable such as x.

The last two digits of our number will look like this:

10x + 6

or this:

10x + 4

I find it easiest to just plug in values from (1-9) for x and see what you get.

If x is 1, the last two digits will be ...56 or ...96

If x is 2, the last two digits will be ...76 or ...76

If x is 3, the last two digits will be ...96 or ...56

If x is 4, the last two digits will be ...16 or ...36

If x is 5, the last two digits will be ...36 or ...16

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We can keep going all the way to x=9, and you will see that the tens digit will always be an odd number...

Therefore the possible values of the tens digit is (1, 3, 5 , 7, 9)

Aug 20, 2020