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
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $12$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $169$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $12$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $169$