To find the unit digit of any number raised to a power, you only need to look at the unit digit of the base. For example, the unit digit of \((123)^2\) is the same as the unit digit of \(3^2\), which is 9.
Step 1: Concept: The unit digit of a power's result is determined solely by the unit digit of the base.
Step 2: Approach: To find the unit digit of \((37)^2\), focus on the base's unit digit, which is 7. Calculate the unit digit of \(7^2\).
Step 3: Explanation: The base is 37; its unit digit is 7. The expression is \((37)^2 = 37 \times 37\). The result's unit digit is the unit digit of the product of the individual unit digits. Unit digit of \((37)^2\) = Unit digit of \((7 \times 7)\). Since \(7 \times 7 = 49\), the unit digit is 9.
Step 4: Answer: The unit digit of \((37)^2\) is 9.