Question

How do you simplify the square root of $36$ using the prime factorization method ?

Answer 1

Hint: The square root of any number is equal to a number, which when squared gives the original number. In mathematics, a square root function is defined as a one-to-one function that takes a positive number as an input and returns the square root of the given input number. We first do the prime factorization of the number and take the factors occurring in pairs outside of the square root radical.

Complete step by step answer:
The number whose square root is to be calculated is $36$. $36$ can be factorized as,
$36 = 2 \times 2 \times 3\times 3$
Now, expressing the prime factorization in powers and exponents, we get,
$36 = {2^2} \times {3^2}$
We can see that $2$ is multiplied twice times and $3$ is also multiplied twice.
Now, $\sqrt {36} = \sqrt {{2^2} \times {3^2}} $
Since we know that ${2^2}$ and ${3^2}$ is a perfect square. So, we can take this outside of the square root we have,
So, $\sqrt {36} = 2 \times 3 $
After multiplication we get,
$ \therefore \sqrt {36} = 6 $

Hence, the square root of $36$ is $6$.

Note: The square root of a perfect square number is easy to calculate using the prime factorisation method. Here $\sqrt {} $ is the radical symbol used to represent the root of numbers. The number under the radical symbol is called radicand. The positive number, when multiplied by itself, represents the square of the number.