Squaring Numbers Ending in 5

Question

Compute 85^2 instantly, and state the general rule for squaring any number ending in 5.

Accepted Answer

Rule: for a number 10a + 5, (10a+5)^2 = 100,a(a+1) + 25. So take the leading digits a, multiply by their successor, and append 25: 85^2: quad 8 times 9 = 72 ;to; mathbf7225. More examples to calibrate: 35^2 = (3times4),25 = 1225; 115^2 = (11 times 12),25 = 13225; 2.5^2 = 6.25 (same rule through the decimal point). Squares unlock fast products via difference-of-squares (see 47 × 53), so the practical drill is: know all squares to 25^2 cold, plus this rule, that covers most of the multiplication you'll face in a trading screen, since you can usually re-center any product onto a known square.

Squaring Numbers Ending in 5

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