<story><title>Squaring two digit numbers in your head</title><url>http://www.jgc.org/blog/2010/03/squaring-two-digit-numbers-in-your-head.html</url><text></text></story><parent_chain></parent_chain><comment><author>ZeroGravitas</author><text>Works even better for squares ending in 5 because you&apos;ll round up and down to multiples of ten which means the number ends in 00 and you&apos;ll always be adding 25.&lt;p&gt;So:&lt;p&gt;&lt;pre&gt;&lt;code&gt;  35 squared is 4x3 x100 = 12 00 + 25 = 1225

  45 squared is 5x4 x100 = 20 00 + 25 = 2025

  55 squared is 6x5 x100 = 30 00 + 25 = 3025
&lt;/code&gt;&lt;/pre&gt;
When I heard about this trick it was referred to as vedic, hindu or indian math, but I don&apos;t know if that&apos;s actually historically/geographically accurate or not. There&apos;s some Japanese nintendo DS games that aim to train you in it, I think it was a bit of a craze over there.</text></comment>
<story><title>Squaring two digit numbers in your head</title><url>http://www.jgc.org/blog/2010/03/squaring-two-digit-numbers-in-your-head.html</url><text></text></story><parent_chain></parent_chain><comment><author>barrkel</author><text>In case this observation isn&apos;t immediately obvious:&lt;p&gt;&lt;pre&gt;&lt;code&gt;    Observe that 27^2 = 30 x 24 + 3^2
&lt;/code&gt;&lt;/pre&gt;
It&apos;s derived from this:&lt;p&gt;&lt;pre&gt;&lt;code&gt;    (x + c)(x - c) = x^2 + cx - cx - c^2
                   = x^2 - c^2
    =&amp;#62; x^2 = (x + c)(x - c) + c^2
&lt;/code&gt;&lt;/pre&gt;
(I note that the blog explains this later, but I had to stop when I read the observation and work it out for myself on paper - when reading the text, it seemed like this step was missing.)</text></comment>