The document provides a method for determining the last digit of the square root of a two-digit number without calculating the full square root. It lists the last digits of the squares of the single-digit numbers from 1 to 9. It then explains that for a two-digit number, the tens place value of the number represents the tens place of the square root, and the last digits of the square root will match one of the single-digit squares. The correct answer can be determined by comparing the original number to the average of the squares of the extreme digits.