Question

How many numbers lie between squares of 12 and 13?

Answer 1

Hint: To solve this problem, we will square the numbers given in the problem (that is 12 and 13). We will then enlist the numbers that lie between them. After then, we can count enlisted numbers.

Complete step-by-step solution -
We will first start by knowing the concepts of squaring a number before we begin to solve the problem. Basically, squaring a number means multiplying a number with itself to get a perfect square (a number which can be expressed as a square of any other number). For example, we have the following numbers (1, 2, 3 and 4). Now squaring them means multiplying these numbers by themselves, doing so, we get $1\times 1=1$, $2\times 2=4$, $3\times 3=9$ and $4\times 4=16$. Now, coming back to the problem in hand, we need to find the numbers that lie between squares of 12 and 13. Thus, we first find the squares of 12 and 13. We have, $12\times 12=144$ and $13\times 13=169$. Now, we need to find the numbers between 144 and 169. The numbers between 144 and 169 are 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167 and 168. We can clearly see that there are 24 numbers (by counting the enlisted numbers).
Hence, there are 24 numbers that lie between the squares of 12 and 13.

Note: An alternative to find the numbers between two numbers say a and b, we use the formula given by (b-a-1). For example, in case of 144 and 169, we can find the numbers between them by using this problem. We have, (169-144-1) = 24.