+0  
 
0
98
3
avatar

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
avatar
0

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

 Aug 20, 2020
 #2
avatar
0

can you explain this

Guest Aug 20, 2020
 #3
avatar+971 
+1

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

.

.

 

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

66 Online Users

avatar
avatar
avatar
avatar