Question

How many natural numbers lie between the square of 17 and 18?

Answer 1

Answer:

there 34 numbers between square of 17 and 18

17 square is 289

18 square is 324

Answer 2

The number of natural numbers lie between the square of 17 and 18 is 34

Given :

The number 17 square and 18 square

To find :

The number of non-square numbers lie between 17 square and 18 square

Concept :

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d

Solution :

Step 1 of 2 :

Here the given numbers are 500² and 501²

17² = 289

18² = 324

The natural numbers lie between 17 square and 18 square are 290 , 291 , 292 , . . . , 323

This is an arithmetic progression

Step 2 of 2 :

Find the number of term

The numbers are 290 , 291 , 292 , . . . , 323

First term = a = 290

Common Difference = d = 291 - 290 = 1

Let 323 is the nth term of the AP

⇒ a + ( n - 1 )d = 323

⇒ 290 + ( n - 1 ) = 323

⇒ n + 289 = 323

⇒ n = 323 - 289

⇒ n = 34

Hence the number of natural numbers lie between the square of 17 and 18 is 34

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