Question

how many numbers lie between the square 13 and 14​

Answer 1

27

13² = 169

14² = 196

So, non square numbers--

= 196 - 169

= 27

So, there are 27 non-squares numbers between 13 square and 14 square...

Answer 2

There are 26 numbers lie between square of numbers 13 and 14

Given :

The square of numbers 13 and 14

To find :

The number of numbers lie between square of numbers 13 and 14

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 13² and 14²

13² = 169

14² = 196

The numbers lie between square of numbers 13 and 14 are 170 , 171 , 172 , ... , 195

This is an arithmetic progression

Step 2 of 3 :

Write down first term and common difference

First term = a = 170

Common Difference = d = 171 - 170 = 1

Step 3 of 3 :

Find the number of terms

Let 3135 is the nth term of the AP

⇒ a + (n - 1)d = 195

⇒ 170 + (n - 1) = 195

⇒ n + 169 = 195

⇒ n = 195 - 169

⇒ n = 26

Hence there are 26 numbers lie between square of numbers 13 and 14

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