Estimate-then-refine: how can you sanity-check a two-digit square fast?

Round to the nearest ten to bracket the answer, then use the exact trick — the estimate catches gross errors.

Before (or after) computing 47², note it's between 40² = 1600 and 50² = 2500, and closer to 2500-ish → expect ~2200. Your exact method gives 2209 — consistent, so you didn't misplace a digit. This pairing (a rough bracket + an exact shortcut) is how you square under time pressure without blundering a place value; the bracket is cheap insurance.