Square 45 instantly

Question

Numbers ending in 5 have the single most useful squaring shortcut in mental math. Solve in your head. What is 45^2? Aim: under 5 seconds.

Accepted Answer

Take the tens digit (4), multiply it by the next integer up (5), and stick "25" on the end: 4 	imes 5 = 20 \ \Rightarrow\ 45^2 = 2025. So 45^2 = \mathbf{2025}. That's it, the last two digits are always 25, and the front is n(n+1) for tens digit n. Why it works: (10n+5)^2 = 100n^2 + 100n + 25 = 100\,n(n+1) + 25. Takeaway. To square a number ending in 5: front digits = n(n+1), back digits = 25. Works for 25, 35, 95, 145, any of them.

Square 45 instantly

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