Question

how many non square numbers lie between the pair of number 500square and 501 square​

Answer 1

There are 1000 non square numbers lie between the pair of number 500 square and 501 square

Given :

The pair of number 500 square and 501 square

To find :

The number of non square numbers lie between the pair of number 500 square and 501 square

Concept :

The nth term of an AP is

aₙ = a + (n - 1 )d.

a = first term

aₙ = nth term

d = common difference.

Solution :

Step 1 of 3 :

Write down the given numbers

Here the given numbers are 500² and 501²

500² = 250000

501² = 251001

The numbers lie between pair of number 500 square and 501 square are 250001 , 250002 , 250003 , ... , 251000

This is an arithmetic progression

Step 2 of 3 :

Write down first term and common difference

First term = a = 250001

Common Difference = d = 250002 - 250001 = 1

Step 3 of 3 :

Find the number of terms

Let 251000 is the nth term of the AP

⇒ a + (n - 1)d = 251000

⇒ 250001 + (n - 1) = 251000

⇒ n + 250000 = 251000

⇒ n = 251000 - 250000

⇒ n = 1000

Hence there are 1000 non square numbers lie between the pair of number 500 square and 501 square

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