Number Line Patterns
1. The image shows three number lines, each with pairs of numbers above and below the line.
2. For each pair, observe the numbers above and below to find a possible relationship.
3. Check if one number in the pair is a perfect square and the other is also a perfect square, to see if there's a connection between their roots.
**First number line:**
- Pairs: (9, 25), (49, 81), (121, 169)
- Roots: $9 = 3^2$, $25 = 5^2$, $49 = 7^2$, $81 = 9^2$, $121 = 11^2$, $169 = 13^2$
- Relationship: The roots above and below are consecutive odd numbers starting at 3 increasing by 2.
**Second number line:**
- Pairs: (4, 16), (36, 64), (100, 144)
- Roots: $4 = 2^2$, $16 = 4^2$, $36 = 6^2$, $64 = 8^2$, $100 = 10^2$, $144 = 12^2$
- Relationship: The roots above and below are consecutive even numbers starting at 2 increasing by 2.
**Third number line:**
- Pairs: (169, 196), (225, 256), (289, 324)
- Roots: $169 = 13^2$, $196 = 14^2$, $225 = 15^2$, $256 = 16^2$, $289 = 17^2$, $324 = 18^2$
- Relationship: The roots above are odd numbers and the roots below are the next consecutive number, increasing by 1.
**Summary:** Each pair consists of perfect squares with roots that follow specific numeric patterns:
- First line: consecutive odd numbers
- Second line: consecutive even numbers
- Third line: consecutive integers increasing by 1
Answer: The boxed pairs highlight these numeric progressions among perfect squares.