Question

How many non perfect square numbers lie between the square of 12003 and 12004​

Answer 1

Given:

Two numbers 12003 and 12004.

To find:

How many non perfect square numbers lie between their squares?

Solution:

First of all, let us take example of smaller numbers to understand better then we will simplify the actual question.

For example, Let us take numbers 5 and 6.

Their squares are 25, 36.

All the numbers between 25 and 36 will be non perfect squares because Square root of a number between 25 and 36 will lie somewhere between 5 and 6 which will be written in decimals.

Numbers between 25 and 36 = {26, 27, 28, 29, 30, 31, 32, 33, 34, 35}

Count of numbers = 10 = 36 - 25 - 1 i.e. Difference of squares minus 1.

Now, let us take the actual numbers:

12003 and 12004.

Applying above Formula:

Count of numbers = Square of 12004 - Square of 12003 - 1

$\Rightarrow 12004^2 - 12003^2-1$

Let us use formula:

$a^2-b^2=(a-b)(a+b)$

$\Rightarrow (12004 - 12003)(12004 + 12003)-1\\\Rightarrow 1(24007)-1\\\Rightarrow 24007-1\\\Rightarrow 24006$

So, the answer is:

There are 24006 non perfect square numbers that lie between the square of 12003 and 12004.