Perfectly Distant Number

Find the root of $2000$

$\sqrt {2000} = 44.7\ldots$

Take the answer and go up to the next integer

$44.7\ldots \Rightarrow 45$

Square that number

$45^2 = 2025$

Subtract $2000$

$2025 - 2000 = 25$

So the answer is $25$

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Proof

Let $a$ be a positive non-integer where $a^2 =$ Chosen number

$x < a < y$

Where $x$ is the nearest integer towards zero and $y$ is the nearest integer away from zero

It stands to reason then that

$x^2 < a^2 < y^2$

So taking the value for $y^2$ should give us the closest perfect square above $a^2$

To find the difference you just

Let $n =$ The answer

$y^2 - a^2 = n$

So applying this to our situation gives us

$45^2 - 2000 = 25$

So it works.

it is remembrance play 2000+25=2025 which is the square of 45

Sq Root 2000 = 44.72

44*44 = 3936

45*45 = 2025

So, Least number to add is 25 to make it complete square.

lets find the least no. to be perfect sq. of 2000

or, by division method, we get 44

therefore, 45 * 45 = 2025

the least no. is 25