Question

how many non perfect squares lie between 1000^2 &1001^2

Answer 1

QUESTION ::

How many non perfect squares lie between ${1000}^{2}$ and ${1001}^{2}$

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ANSWER ::

★Here we have to find out the number of non-square numbers between ${1000}^{2}$ and ${1001}^{2}$

★So, let 1000 be ‘n’ and 1001 be ‘n+1’

★The process to find out non-square numbers between ${n}^{2}$ and ${(n \:+\:1)}^{2}$ is :-
➡(2 × n) + 1 = 2n + 1

★So the number of non-square numbers between ${1000}^{2}$ and ${1001}^{2}$ = (2 × 1000 ) + 1.
= 2000 + 1
= 2001.

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$\textbf{\underline{CHECKING}}$

$1000^2$
= 1000 × 1000
= 10,00,000.

$1001^2$
= 1001 × 1001
= 10,02,001.

★10,02,001 - 10,00,000
=2001.

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$\textbf{SO YOUR ANSWER IS :-}$
➡ 2001.