Question

What’s the square root of $3721$ ?

Answer 1

Hint: First, we need to know about the concept of the square root. The square root of the number is a value, which on multiplied by itself given the original number, which is the given numbers that obtain by multiplying any of the whole numbers (zero to infinity) twice, or the square of the given numbers yields a whole number like \[\sqrt 9 = {\sqrt 3 ^2} = 3\]

Complete step-by-step solution:
We also need to know about the concept of prime factorization. Prime numbers are the numbers that are divisible by themselves and $1$ only or also known as the numbers whose factors are the given number itself.
But the composite numbers which are divisible by themselves, $1$ and also with some other numbers (at least one number other than $1$ and itself)
Every composite number can be represented in the form of prime factorization.
Since from the given that we asked to find the square root of $3721$
If the given number is prime then we cannot able to find its prime factorization. Now to check the given number is prime or composite.
Since Prime numbers are the numbers that are divisible by themselves and $1$ only. But the number $3721$ can be divisible by $61$ and thus which is a composite number.
Since $3721$ is a composite that is divided by the number $61$ and now separates that into rewrite the number as to $3721 = 61 \times 61$ where $61$ is prime so don’t change that. (suppose not, then we again need to prime factorize the founded number)
Which can be rewritten as in the multiplication form of $3721 = {61^2}$
Taking the common square root of both sides we get $\sqrt {3721} = \sqrt {{{61}^2}} \Rightarrow 61$
Therefore, the square root of \[3721\] is $61$

Note: To find the factors, find the smallest prime number that divides the given number and divide it by that number and then again find the smallest prime and the process continues. The set to each other to form the bigger number are called the factors. And $\sqrt {} $ is known as the radical symbol.
We can find whether the given number is prime or composite by the trial-and-error methods. Divide the number with the prime numbers less than the given number. if the number is exactly divisible by the prime number, it is the composite number, if not then it is the prime number.
The only even prime number is $2$ and all other prime numbers are odd.