Question

How many natural numbers lie between the squares of 22 and 23?

Answer 1

Step-by-step explanation:

To find the number of natural numbers between square of 23 and square of 24, we need to find the values of squares of 23 and 24. Hence, So the square of 23 is 529 and the square of 24 is 576.

Answer 2

SOLUTION

TO DETERMINE

The number of natural numbers lie between 22 square and 23 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 22² and 23²

22² = 484

23² = 529

The natural numbers lie between 19 square and 20 square are 485 , 486 , 487 , . . . , 528

This is an arithmetic progression

First term = a = 485

Common Difference = d = 486 - 485 = 1

Let 528 is the nth term of the AP

⇒ a + ( n - 1 )d = 528

⇒ 485 + ( n - 1 ) = 528

⇒ n + 484 = 528

⇒ n = 528 - 484

⇒ n = 44

FINAL ANSWER

The number of natural numbers lie between 22 square and 23 square = 44

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