Question

How many natural numbers lie between 8 square and 9 square

Answer 1

SOLUTION

TO DETERMINE

The number of natural numbers lie between 19 square and 20 square

CONCEPT TO BE IMPLEMENTED

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d

EVALUATION

Here the given numbers are 8² and 9²

8² = 64

9² = 81

The natural numbers lie between 8 square and 9 square are 65 , 66 , 67 , . . . . , 80

This is an arithmetic progression

First term = a = 65

Common Difference = d = 66 - 65 = 1

Let 80 is the nth term of the AP

⇒ a + ( n - 1 )d = 80

⇒ 65 + ( n - 1 ) = 80

⇒ n + 64 = 80

⇒ n = 80 - 64

⇒ n = 16

FINAL ANSWER

The number of natural numbers lie between 8 square and 9 square = 16

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