Directions: Find the odd man out: 16, 25, 36, 72, 144, 196, 225

### Concept & Perfect Squares The sequence consists of perfect squares of integers. Recognizing squares is key to instantly solving this type of grouping question. ### Step-by-Step Solution 1. Let's list the given numbers: $16, 25, 36, 72, 144, 196, 225$. 2. Identify the root of each number: - $16 = 4^2$ - $25 = 5^2$ - $36 = 6^2$ - $144 = 12^2$ - $196 = 14^2$ - $225 = 15^2$ 3. Evaluate $72$. The square root of $72$ is not an integer ($8^2=64, 9^2=81$). 4. Therefore, $72$ is not a perfect square, making it the odd man out. ### Exam Strategy & Shortcut If you have memorized squares up to $20$, you can scan the list and immediately pick out $72$ as the anomaly in under $5$ seconds. ### Common Pitfall Students sometimes mistakenly think $72$ fits because they confuse it with other powers or multiples (like $36 \times 2$), losing sight of the overarching "perfect square" theme. ### Final Answer Therefore, the correct answer is **72**.