Question

How many numbers lie in between the square of the following numbers?
A) $12\,and\,13$
B) $25\,\,and\,26$
C) $99\,and\,100$

Answer 1

Hint: In order to find the correct answer, first find the squares of both the numbers given in the options of the question. Then, find the difference between the squares of both the numbers. Now, subtract 1 from the difference. This is the required answer.

Complete step-by-step answer:
To solve this question, we will take the options one by one. So, firstly, we will take option (i).
A) We have the numbers $12\,and\,13$.
First, we will find the squares of both the numbers.
So, the square of 12.
${12^2} = 144$
The square from 13.
${13^2} = 169$
The difference between the squares of the two numbers is
$169 - 144$
$ = 25$
Now, we have to find the numbers between them, but in this One of the numbers is included. So, we will subtract 1 from the result. To get the correct answer.
Therefore, the numbers between $12\,and\,13$ is given as:
$ = 25 - 1$
$ = 24$.
B) We have the numbers $25\,and\,26\,$.
First, we will find the squares of both the numbers.
So, the square of 25.
${25^2} = 625$
The square from 26.
${26^2} = 676$
The difference between the squares of the two numbers is
$676 - 625$
$ = 51$
Now, we have to find the numbers between them, but in this One of the numbers is included. So, we will subtract 1 from the result. To get the correct answer.
Therefore, the numbers between $25\,and\,26$ is given as:
$ = 51 - 1$
$ = 50$.
C) We have the numbers $99\,and\,100$.
First, we will find the squares of both the numbers.
So, the square of 99.
${99^2} = 9801$
The square from 100.
${100^2} = 10000$
The difference between the squares of the two numbers is
$10000 - 9801$
$ = 199$
Now, we have to find the numbers between them, but in this One of the numbers is included. So, we will subtract 1 from the result. To get the correct answer.
Therefore, the numbers between $99\,and\,100$ is given as:
$ = 199 - 1$
$ = 198$.

Note: You must be very clear with the concepts. This type of question requires tricks to get solved. You can also write the numbers between the squares of the two numbers. And then count the number which comes in between the squares of the two numbers.