Question

How many non-perfect squares are there between squares of 37 and 38?

Answer 1

Given : squares of 37 and 38

To Find :  How many non-perfect squares are there between squares of 37 and 38

Solution:

non-perfect squares   there between squares of 37 and 38

= 38² - 37²  - 1

= (38 + 37) (38 - 37) - 1

= 75(1) - 1

= 74

There are 74  non-perfect squares are there between squares of 37 and 38

non-perfect squares are there between squares of n and (n+1) are given by 2n

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Answer 2

SOLUTION

TO DETERMINE

The number of non-perfect squares are there between squares of 37 and 38

EVALUATION

We have to find the number of non-perfect squares are there between squares of 37 and 38

37² = 1369

38² = 1444

The non perfect square number between squares of 37 and 38 are

1370 , 1371 , 1372 , .... , 1443

This is an arithmetic progression

First term = a = 1370

Common Difference = d = 1371 - 1370 = 1

Let 1443 is the n th term of the AP

So by the given condition

$\sf{a + (n - 1)d = 1443}$

$\sf{ \implies \: 1370 + (n - 1)= 1443}$

$\sf{ \implies \: n + 1369= 1443}$

$\sf{ \implies \: n = 1443 - 1369}$

$\sf{ \implies \: n = 74}$

FINAL ANSWER

The number of non-perfect squares are there between squares of 37 and 38 = 74

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