Question

How do you find the simplest radical form of $12$ ?

Answer 1

Hint:
First, we need to find the factors of the given number to calculate the square root. Factors are the number that completely divides the number without leaving any remainder behind. The square root of a $\sqrt {12} $ can be calculated by prime factorization of the number. Prime factorization is defined as expressing a number as a product of prime numbers. The numbers which are divisible by one and itself, i.e., it should only have two factors are called prime numbers.

Complete Step By Step:
Given the number to simplify is $\sqrt {12} $
First, we will find the square root of $12$ by finding its prime factors. The square root of a number can be simplified by prime factorization of the number.
Prime factorization involves expressing a number as a product of prime numbers.
The prime factor of $12$
$
  2|12 \\
  2|6 \\
  3 \\
$
Hence the factor of $\left( {12} \right) = 2 \times 2 \times 3$
Now we will pair the similar factors in a group of two,
Therefore,
$
  \sqrt {12} = \sqrt {2 \times 2 \times 3} \\
   \Rightarrow \sqrt {12} = \sqrt {{2^2} \times 3} \\
$
After forming a pair of the similar factors, we will take a pair out of the square root and thus, continue this process to simplify and attain the answer.
$ \Rightarrow \sqrt {12} = 2\sqrt 3 $

Hence, we get the square root of $12$ is $2\sqrt 3 $

Note:
The square root of any number is calculated by prime factorization of the number. After prime factorization which involves expressing a number as a product of prime numbers (numbers which are divisible by and itself), we need to pair similar factors in a group of two. Another way to simplify the square root of any number is by using the long division method, which is quite complex, and thus, the chances of getting any error are high.