Square of Reversal of Small-Digit Number/Examples/13

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Example of Square of Reversal of Small-Digit Number

$13^2 = 169$
$31^2 = 961$


Proof

\(\ds 13^2\) \(=\) \(\ds \paren {10 + 3}^2\)
\(\ds \) \(=\) \(\ds 10^2 + 2 \times 10 \times 3 + 3^2\)
\(\ds \) \(=\) \(\ds 100 + 60 + 9\)
\(\ds \) \(=\) \(\ds 169\)


\(\ds 31^2\) \(=\) \(\ds \paren {30 + 1}^2\)
\(\ds \) \(=\) \(\ds 30^2 + 2 \times 30 \times 1 + 1^2\)
\(\ds \) \(=\) \(\ds 900 + 60 + 1\)
\(\ds \) \(=\) \(\ds 961\)

$\blacksquare$


Sources