Which of the squares (123², 57², 92², 61², 209²) will end with the digit 1?

Yes, it is the correct option. For this problem, you don't need to calculate the full value of the square of the given number. Just pick the digit in units place in each number and multiply it with itself. Lets do it for all the given numbers: 123²: 3 x 3 = 9          So, it will not end with 1 57² : 7 x 7 = 49        So, it will not end with 1 92² : 2 x 2 = 4           So, it will not end with 1 61²   :  1 x 1 = 1        Yes, it will end with 1 209² : 9 x 9 = 81       Yes, it will end with 1