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The difference of two consecutive perfect squares is 21. What is the largest of the two perfect squares?

Sagot :

Mhanifaidn

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:

  • (n+1)² - n² = 21

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.

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