Answer:
76.
Step-by-step explanation:
It is given that N is a 2-digit number.
Last two digits of N^2 is the same as N.
We know that, a number is even if it ends with 0,2,4,6,8.
[tex]2^2=4,4^2=16,6^2=36,8^2=64[/tex]
If 0 is in end then we get two zeros in the square of that number.
It is clear that, number should ends with 6 to get the same number at the end.
[tex]16^2=256[/tex]
[tex]26^2=676[/tex]
[tex]36^2=1296[/tex]
[tex]46^2=2116[/tex]
[tex]56^2=3136[/tex]
[tex]66^2=4356[/tex]
[tex]76^2=5776[/tex]
[tex]86^2=7396[/tex]
[tex]96^2=9216[/tex]
It is clear that last two digits of (76)^2 is the same as 76.
Therefore, the required number is 76.
