Question

For how many natural numbers N is N² - 200 a perfect square?​

Answer 1

Step-by-step explanation:

Both n

2

and (n+1)

2

are perfect square numbers and they are consecutive perfect squares.

⇒ All the numbers between them are non-perfect square.

Numbers between n

2

and (n+1)

2

are

=(n+1)

2

−n

2

−1

=n

2

+2n+1−n

2

−1

=2n

⇒ There are 2n non-perfect square numbers.

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