Squares Worth Knowing

Memorizing perfect squares up to 20 pays off constantly in math. Twelve squared is 144, thirteen squared is 169, fourteen squared is 196, fifteen squared is 225. These anchor points let you estimate nearby squares — need 14.5 squared? It falls between 196 and 225, roughly 210 (actual: 210.25).

A useful pattern: the difference between consecutive squares increases by 2 each time. 5² - 4² = 9, 6² - 5² = 11, 7² - 6² = 13. This happens because (n+1)² - n² = 2n + 1 — always an odd number. Knowing this, you can build new squares from ones you already know.