The square of a whole number ends in the digit 6. The number itself must end in:

The last digit of a square depends only on the last digit of the number: 0→0, 1→1, 2→4, 3→9, 4→6, 5→5, 6→6, 7→9, 8→4, 9→1. Only 4 and 6 produce a square ending in 6 — for example $14^2=196$ and $16^2=256$. Digits 2 and 8 give squares ending in 4, not 6.