121
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Let the smaller perfect square be n² and the larger perfect square be (n+1)².
The difference between these squares is given by:
Expanding and simplifying the equation:
- n² + 2n + 1 - n² = 21
- 2n + 1 = 21
- 2n = 20
- n = 10
The smaller perfect square is n² = 10² = 100, and the larger perfect square is (n+1)² = 11² = 121.
Therefore, the largest of the two perfect squares is 121.
