Mental squares
You already know plenty of squares: 20², 25², 50²… The trick is to use them as anchors and correct outward — the same round-and-correct idea that makes ×98 easy.
Two methods here (near-a-known-square, and the 50-base method) plus the ending-in-5 rule cover most squares you will ever meet.
Method 1 · Level 2
Squares Near a Known Square: n±1 and n±2
(n + 1)² = n² + 2n + 1: 41² = 1,600 + 80 + 1 = 1,681. (n − 2)² = n² − 4n + 4.
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Method 2 · Level 3The 50-Base Method: Squares of the 40s, 50s and 60s
(50 ± d)² = 2,500 ± 100d + d²: 53² = 2,500 + 300 + 9 = 2,809.
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