Question

How many natural numbers lie between the square of natural number n and n+1?​

Answer 1

Answer:

this is answer of your question

Answer 2

Given:

Square of natural number n and (n+1)

To find:

natural numbers lying between the two numbers.

Solution:

The squares of numbers n and (n+1) are consecutive perfect squares.

⇒ The numbers that would be lying between the two squares will be a non-perfect squares.

Thus, numbers lying between n² and (n+1)² are

⇒ (n+1)² - n² - 1

⇒ n² + 2n + 1 - n² - 1

Cancelling the postive and negative terms we get,

⇒ 2n.

∴ 2n numbers will be lying between n² and (n+1)².