Square 203 around a round base

Question

203 hugs the round base 200, whose square is easy. One expansion does it. Solve in your head. What is 203^2? Aim: under 12 seconds.

Accepted Answer

Expand around 200 with (200+3)^2 = 200^2 + 2\cdot 200 \cdot 3 + 3^2: 203^2 = 40000 + 1200 + 9 = 41209. So 203^2 = \mathbf{41209}. Running total: "forty thousand… forty-one two hundred… forty-one two-oh-nine." Slide-method check: 203^2 = 206 	imes 200 + 9 = 41200 + 9 = 41209. Same answer. Takeaway. For a number near a round base b, (b+d)^2 = b^2 + 2bd + d^2 is one line. The cross term 2bd is the only piece that needs any thought.

Square 203 around a round base

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