🧱 See It
Arrange 16 tiles into equal rows and columns and they form an actual square — 4 rows of 4:
4 × 4 = 16. Because it makes a real square shape, 16 is called a "perfect square."
✏️ Draw It
A square root asks the reverse question: "what side length makes this square?"
| Side length | 2 | 3 | 4 | 5 |
|---|---|---|---|---|
| Square (area) | 4 | 9 | 16 | 25 |
Reading left to right: squaring. Reading right to left: taking the square root.
🔢 Write It
4² = 16 (four squared)
√16 = 4 (the square root of sixteen)
Squaring and square-rooting are opposite moves — exactly like multiplication and division undo each other.
💡 Worked Examples
Example 1 — Square a number: 7²
- Squaring means "times itself":
7 × 7 - Answer:
49
Example 2 — Find a square root: √81
- Ask: "what number times itself makes 81?"
- Check
9 × 9 = 81— that's it. - Answer:
√81 = 9
🧠 Quick Reference
| n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| n² | 1 | 4 | 9 | 16 | 25 | 36 | 49 | 64 | 81 | 100 | 121 | 144 |
Knowing these twelve by heart turns most square roots into a quick lookup instead of a guessing game.