At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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

Sagot :

121

=====================

Let the smaller perfect square be 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.