Question

How many non perfect square numbers lie between the squares of 12 and 13

Answer 1

The number of non square numbers

between n² and ( n + 1 )² is 2n

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Here ,

n = 12 ,

n + 1 = 13

Therefore ,

Number of natural numbers lie

between 12² and 13² = 2 × 12

= 24

Answer 2

The number of non perfect square numbers lie between the squares of 12 and 13 is 24

Given :

The number 12 square and 13 square

To find :

The number of non perfect square numbers lie between the squares of 12 and 13

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 12² and 13²

12² = 144

13² = 169

The natural numbers lie between 12 square and 13 square are 145 , 146 , 147 , ... , 168

This is an arithmetic progression

Step 2 of 2 :

Find the number of term

The numbers are 145 , 146 , 147 , ... , 168

First term = a = 145

Common Difference = d = 146 - 145 = 1

Let 251000 is the nth term of the AP

⇒ a + (n - 1)d = 168

⇒ 145 + (n - 1) = 168

⇒ n + 144 = 168

⇒ n = 168 - 144

⇒ n = 24

Hence the number of non perfect square numbers lie between the squares of 12 and 13 is 24

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