Question

How many non-square numbers lie between 500 square and 501 square

Answer 1

Answer:

The formula for finding the number of non square numbers are -2n

Therefore there will be=2 multiple by 500= 1000 non square numbers

is it correct (check between 500sq =250000,. 501 sq= 251001)

Answer 2

The number of non-square numbers lie between 500 square and 501 square is 1000

Given :

The number 500 square and 501 square

To find :

The number of non-square numbers lie between 500 square and 501 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

500² = 250000

501² = 251001

The natural numbers lie between 500 square and 501 square are 250001 , 250002 , 250003 , ... , 251000

This is an arithmetic progression

Step 2 of 2 :

Find the number of term

The numbers are 250001 , 250002 , 250003 , ... , 251000

First term = a = 250001

Common Difference = d = 250002 - 250001 = 1

Let 251000 is the nth term of the AP

⇒ a + ( n - 1 )d = 251000

⇒ 250001 + ( n - 1 ) = 399

⇒ n + 250000 = 251000

⇒ n = 251000 - 250000

⇒ n = 1000

The number of non-square numbers lie between 500 square and 501 square is 1000

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