Henry Ernest Dudeney/Puzzles and Curious Problems/125 - Accommodating Squares/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $125$

Accommodating Squares

Can you find two three-digit square numbers (no noughts) that, when put together, will form a six-digit square number?

Thus, $324$ and $900$ (the squares of $18$ and $30$) make $324 \, 900$, the square of $570$, only there it happens there are two noughts.

There is only one answer.

Solution

$475^2 = 225 \, 625$, while $15^2 = 225$ and $25^2 = 625$.

Also see

• Squares whose Digits can be Separated into 2 other Squares
• 475
• On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008): A048375

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $125$. -- Accommodating Squares
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $198$. Accommodating Squares