Finding the Number of Natural Numbers between 8^2 and 9^2

To find the number of natural numbers between 8^2 and 9^2, we need to follow some simple steps:

Step 1: Calculate the values of 8^2 and 9^2
8^2 = 64
9^2 = 81

Step 2: Determine the first natural number greater than 64
The first natural number greater than 64 is 65.

Step 3: Determine the last natural number less than 81
The last natural number less than 81 is 80.

Step 4: Subtract the first natural number from the last natural number
80 - 65 = 15

Therefore, there are 15 natural numbers between 8^2 and 9^2.

Formula: The formula to find the number of natural numbers between two perfect squares is given as:
Number of natural numbers = (Second perfect square root - First perfect square root) - 1

where,
First perfect square root = square root of the smaller perfect square
Second perfect square root = square root of the larger perfect square

Using this formula, we can find the number of natural numbers between any two perfect squares.

Example: Find the number of natural numbers between 11^2 and 12^2
11^2 = 121
12^2 = 144

First perfect square root = square root of 121 = 11
Second perfect square root = square root of 144 = 12

Number of natural numbers = (12 - 11) - 1 = 0

Therefore, there are 0 natural numbers between 11^2 and 12^2.

There are 16 natural numbers between 8^2 and 9^2.

We know that, between any two perfect squares, there are 2n natural numbers, where n= smaller number.
so, here n= 8,so 2n = 16. Therefore 16 natural numbers lie between 8^2 and 9^2