Question

How many non square numbers are between 29 square and 30 square

Answer 1

non square numbers between
${29}^{2}$
and
${30}^{2}$
is 29×2 = 58

so there are 58 numbers present in between 29square and 30 square

hope it helps you.

Answer 2

The number of non-square numbers lie between 29 square and 30 square is 58

Given :

The number 29 square and 30 square

To find :

The number of non-square numbers lie between 29 square and 30 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 :

Write down the given numbers

Here the given numbers are 29² and 30²

29² = 841

30² = 900

The natural numbers lie between 29 square and 30 square are 842 , 843 , 844 , ... , 899

This is an arithmetic progression

Step 2 of 2 :

Find the number of term

The numbers are 842 , 843 , 844 , ... , 899

First term = a = 842

Common Difference = d = 843 - 842 = 1

Let 899 is the nth term of the AP

⇒ a + ( n - 1 )d = 899

⇒ 842 + ( n - 1 ) = 899

⇒ n + 841 = 899

⇒ n = 899 - 841

⇒ n = 58

The number of non-square numbers lie between 29 square and 30 square is 58

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