Square 995, a big number with a tiny correction

Question

995 is 5 below 1000 and also ends in 5, so two mental tricks both crack it fast. Solve in your head. What is 995^2? Aim: under 15 seconds.

Accepted Answer

Slide to the round base 1000 using n^2 = (n-d)(n+d) + d^2 with d = 5: 995^2 = 990 	imes 1000 + 5^2 = 990000 + 25 = 990025. So 995^2 = \mathbf{990025}. The ends-in-5 rule agrees: leading number 99, times 100 = 9900, append 25 → 990025. Expansion check: (1000 - 5)^2 = 1{,}000{,}000 - 10{,}000 + 25 = 990025. Confirmed. Takeaway. Numbers near 1000 square via the slide (n-d)(n+d) + d^2, one round product plus a small square. When they also end in 5, the two shortcuts cross-check each other.

Square 995, a big number with a tiny correction

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