Question

How do you find the square root of $13?$ .

Answer 1

Hint: The given problem is based on square root. To find the square root we use the Prime factorization method. L.C.M of the given number has been taken. In L.C.M. we have to check if the given number is divisible of any other number or not. Then we continue the process until $1$ is reached. Then by making a pair we are finding the number which is the square root of the given number.

Complete step-by-step answer:
In mathematics, a square root of a number $x$ is a number $y$ such that ${y^2} = x$ . Like $x$ is $2$ then $y$ be ${2^2} = 4$
Consider a number which is multiplied by itself is called the square root.
We can find the square root of a number by prime factorization method.
In prime factorization method making the factors of a given number by taking L.C.M.
L.C.M. is the least common multiple.
For the given question we have given the number $13$ for solving that taking there L.C.M.
In L.C.M. we consider a number and check it is divisible by $13$ or not. If it is divisible then write its quotient, again we continue that process so on….
As is a prime number as prime number are those numbers which can be divisible by itself. So, $13$ is divisible by itself. So the L.C.M. of $13$ be.
The numbers we get are $13,1$
Multiply we get $13 \times 1$
So, there is no pairs of number occur $13$ is left only as Single number
So, $13$ is a Prime number, there is not simpler form for its square root as $\left| \!{\overline {\,
 {13} \,}} \right. $ is not a perfect square root

Note: In mathematical square root frequently appear in formulas as well as in many physical laws Civil Engineers use square root when they build roads coming off of a lull side. The above equation is also based on square roots; we are using a prime factorization method to solve it.