Question

Rehan says there are 37 non square numbers between 9 squars and 11 square . Is he right

Answer 1

SOLUTION

TO CHECK

Rehan says there are 37 non square numbers between 9 squares and 11 square . Is he right

EVALUATION

Here

${9}^{2} = 81$

${11}^{2} = 121$

Now the numbers between 81 and 121 are

82 , 83 , 84 ,..., 120

This is an arithmetic progression

First term = a = 82

Common Difference = d = 83 - 82 = 1

Let 120 be the n th term

So by the given condition

$\sf{82 + (n - 1) =120 }$

$\sf{ \implies \: (n - 1) =38 }$

$\sf{ \implies \: n = 39}$

Now there is one square number between 9² and 11² is 10²

Hence the number of non square numbers between 9 squares and 11 square is

= 39 - 1

= 38

Hence Rehan was wrong

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