The Last One is 6

It is easy to see that in order to have a perfect square with 6 as the last digit, we have to square a number ending in either 4 or 6.

We need to find the maximum integer ending in either 4 or 6 such that the square is less than 1000.

By checking:

36 x 36 = 1296

so the maximum number ending in 6 is 26.

34 x 34 = 1156

so the maximum number ending in 4 is 24.

Therefore we have: 4, 14, 24 6, 16, 26

So we have 6 numbers.

Square of an integer less than 1000 end with the digit 6 are : 16(4x4), 36(6x6), 196(14x14), 256(16x16), 576(24x24), 676(26x26

find digits in the ones that would have a "6" in the end when squared. these digits would be 4 and 6.

thus; 4, 6 , 14 , 16, 24 , 26 when squared would have a '6' in the end.

numbers are square of number having last digit as 6 and 4 so numbers are, 4,6,14,16,24,26

4^2, 6^2, 14^2,16^2, 24^2, 26^2

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^ = is to the power of

When $n^{2}$ ends with the digit 6,the unit digit of n is either 4 or 6.

$4^{2}$ =16

$6^{2}$ =36

$14^{2}$ =196

$16^{2}$ =256

$24^{2}$ =576

$26^{2}$ =676

$34^{2}$ =1156>1000

So,n can be 4,6,14,16,24,26.

Ans=6