Question

The square root of $387$ must be a number between what two numbers?

Answer 1

Hint: In this question, we are given a number for which we have to find two numbers between which its square root will lie.
This can be done by two methods, one is the ‘hit and trial’ method, i.e., check the square of each natural number and find the two numbers and another is, try to find the square root of the given number, which will give us the exact square root and then easily we can find the two numbers.

Complete answer:
The given number is $387$ .
To find two numbers between which its square root will lie.
So, we will do it by the second method i.e., first, we will find its exact square root using the long division method.
First, make pairs of the digits in the given number, starting from the backside i.e., $\overline 3 \overline {87} $ . Since, there are only three digits, so $3$ will be left alone.
Now, when we divide this number using long the division method, we will get, $\sqrt {387} = 19.673$ , which is clearly between $19$ and $20$ , i.e., $19 < \sqrt {387} < 20$ .
Hence, the two numbers between which square root of $387$ lies are $19$ and $20$ .

Note:
Another way to do this question is hit and trial method, in which, one has to check the square of each natural number starting from $1$ and find the two numbers or directly, we can see that ${20^2} = 400$ , which is greater than $387$ and is not so far from $387$ , whereas, ${19^2} = 361$ , which is less than $387$ . Hence, $19 < \sqrt {387} < 20$ .
In the long division method for finding the square root, making pairs is an important step and pairs should be made starting from the back.
The ‘Hit and trial’ method is time-consuming but is easier than the other method.