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?

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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 - 7 years, 1 month ago

You may be interested in knowing that square of $\color{#D61F06}{any}$ 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 $37^2 = \color{#D61F06}{9} \color{#3D99F6}{49} +20*21 = 1369. ~~~~~~~~~~~~~~~(40 - 3)^2 = \color{#D61F06}{16} \color{#3D99F6}{09} -20*12=1369\\ Three ~digit~ number ~the ~same ~way~~\\127^2 = \color{#D61F06}{144} \color{#3D99F6}{49} +20*84=16129 ~~~~~~~~~~~~~~~~~~~~(130-3)^2 = \color{#D61F06}{169} \color{#3D99F6}{09} -20*39=16129\\ With~ unit~ digit~ \color{#20A900}{ 5}........ (10a + 5)^2 =\color{#3D99F6}{a*(a+1)}25...........(125)^2=\color{#3D99F6}{(12*13)}25 = \color{#3D99F6}{156}25$

Niranjan Khanderia - 6 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$