Square of Reversal of Small-Digit Number/Examples/12
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Example of Square of Reversal of Small-Digit Number
- $12^2 = 144$
- $21^2 = 441$
Proof
| \(\ds 12^2\) | \(=\) | \(\ds \paren {10 + 2}^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 10^2 + 2 \times 10 \times 2 + 2^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 100 + 40 + 4\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 144\) |
| \(\ds 21^2\) | \(=\) | \(\ds \paren {20 + 1}^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 20^2 + 2 \times 20 \times 1 + 1^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 400 + 40 + 1\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 441\) |
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $12$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $144$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $12$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $144$