Square 75 in your head

Question

Traders quote 75^2 without pausing because the ends-in-5 rule makes it automatic. Solve in your head. What is 75^2? Aim: under 6 seconds.

Accepted Answer

Tens digit is 7; multiply it by 8 (the next integer), then append 25: 7 	imes 8 = 56 \ \Rightarrow\ 75^2 = 5625. So 75^2 = \mathbf{5625}. Front part 56, back part 25, glued together. Check by expansion: 75^2 = (70+5)^2 = 4900 + 700 + 25 = 5625. Confirmed. Takeaway. Ends-in-5 squaring: n(n+1) up front, 25 in back. Memorising 7	imes 8 = 56 makes 75^2 = 5625 a reflex.

Square 75 in your head

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