Video narration
Can two triangular numbers really make a square number? Imagine counters on a small game grid. A square number makes equal rows and columns; a triangular number arranges dots in a triangle. Three green dots form two rows: one, then two. This is the second triangular number, so it equals three. On the right, six blue dots form three rows: one, two, and three. This is the third triangular number, so it equals six. Now watch the separate patterns join. The blue triangle flips and slides into the green one. The dots lock together in three equal rows of three-a perfect square grid. So your counters show three plus six equals nine. And nine is three times three, or three squared. So yes: these sequences connect-three plus six equals nine, which is three squared.