Question

What is the rule to find the number of numbers between perfect squares? [2 MARKS]

Answer 1

Concept : 1 Mark
Condition : 1 Mark

In general we can say that there are 2n non-perfect square numbers between the squares of the numbers n and (n + 1).

For example consider,

$n=4andn+1=5$

$4^2=16and{5}^2=25$

The numbers between 16 and 25 are 17,18,19,20,21,22,23,24. i.e., 8 numbers

Now, $8=2\times 4$

$\Rightarrow$ There are 2n non-perfect square numbers between the squares of the numbers n and (n + 1).