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Quick Calculations 3: Squaring numbers

Who knows? One strategy for numbers close to a multiple of 10 is to rewrite it in the form \( (10m \pm n) ^ 2 \), then factor this. Reliable, or not?

Note by David Lee
3 years, 7 months ago

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Very reliable. For example, squaring \(99\) can be very tedious. However, rewriting it as \((100-1)^{2}\) would yield \(10000+1-200\), which can be very easily solved to \(\boxed{9801}\). Thus, the best way to simplify squaring is by making it simple addition, or simple multiplication.

Nanayaranaraknas Vahdam - 3 years, 7 months ago

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You may be interested in knowing that square of \(\color{red}{any} \) two and three digit numbers can be found as under. \( (10a\pm b)^2\) write square of a and then of b. (if b is 1, 2 , or 3, write its square as 01, 04 or09) to this \(\pm\) 20 times a*b. Say \(37^2 = \color{red}{9} \color{blue}{49} +20*21 = 1369. ~~~~~~~~~~~~~~~(40 - 3)^2 = \color{red}{16} \color{blue}{09} -20*12=1369\\ Three ~digit~ number ~the ~same ~way~~\\127^2 = \color{red}{144} \color{blue}{49} +20*84=16129 ~~~~~~~~~~~~~~~~~~~~(130-3)^2 = \color{red}{169} \color{blue}{09} -20*39=16129\\ With~ unit~ digit~ \color{green}{ 5}........ (10a + 5)^2 =\color{blue}{a*(a+1)}25...........(125)^2=\color{blue}{(12*13)}25 = \color{blue}{156}25 \)

Niranjan Khanderia - 2 years, 11 months ago

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