Question

how many natural no. lie between 100sq. and 101 sq.​

Answer 1

Short method...

     

Let two consecutive integers = n, n + 1.

Their sums = n², (n + 1)²

No. of natural numbers between any two integers is 1 subtracted from the difference of those numbers.

Thus,

$\mapsto\ (n+1)^2-n^2-1 \\ \\ \mapsto\ n^2+2n+1-n^2-1 \\ \\ \mapsto\ 2n$

Such that,

No. of natural numbers between squares of any two consecutive integers is double the lowest integer.

According to this...

Let n = 100, thus n + 1 = 101

So, no. of natural numbers between 100² and 101² = 2n = 2 × 100 = '200'