Question

How many numbers lie between the square of the numbers: 107 and 108?

Answer 1

Hint: In the question, we notice that the first number and the the second number is in the form of '$n $'  and ‘$(n+1)$’. Then according to the question, we have to find how many numbers lie between ${n^2}$ and ${(n + 1)^2}$. We can find the answer by using a formula. So, we have a simple formula for solving this question.
Numbers lie between ${n^2}$ and ${(n + 1)^2} = 2n$
We have an alternative method for solving this question where we can find the square of both the numbers and then find how many numbers lie between them.

Complete step by step solution:
The given numbers are $107$ and $108$.
We need to find the number of numbers lying between the squares of these two numbers.
Here $n = 107$ and $(n+1) = 108$
Now, we will use the above formula that is;
Numbers lie between ${n^2}$ and ${(n + 1)^2} = 2n$
Numbers lie between ${107^2}$and ${108^2} = 2 \times 107$
$ = 214$

$\therefore $The numbers lie between ${107^2}$and ${108^2}$ = 214.

Note: We can also use an alternative method to calculate the numbers lie between the squares of two numbers.

Let's find the square of the given numbers:

$107^2 =11449$

$108^2=11664$

Now we have to calculate the numbers present between $11449 $ to $11664$.

So, the number of numbers present $= 11664-11449-1$

$=215-1$

$=214$

Therefore, 214 numbers are present between $107^2$ and $108^2$.

This method is not practical because it can consume time. So, the first method is preferable for this type of cases.