Question

What is the square root of $28$ in simplified radical form?

Answer 1

Hint: In this question we have been given with the number $28$ and we have to find the square root of the given number in a simplified radical format. We will use the method of prime factorization to get the required solution. We will first write the number $28$ in terms of the multiplication of its prime numbers and then we will multiply a single term if there are two instances of it in multiplication. After removing the terms from the square root, we will multiply them to get the required solution.

Complete step-by-step solution:
We have the number given to us as:
$\Rightarrow 28$
Since we have to find its square root, the number can be written as:
$\Rightarrow \sqrt{28}$
Now we know that the number $28$ is divisible by $2$ and it can be written as $2\times 14$therefore, on substituting, we get:
$\Rightarrow \sqrt{2\times 14}$
Now we know that the number $14$ is divisible by $2$ and it can be written as $2\times 7$ therefore, on substituting, we get:
$\Rightarrow \sqrt{2\times 2\times 7}$
We can see that there are two instances of the number $2$ in the square root therefore, on taking it out of the square root, we get:
$\Rightarrow 2\sqrt{7}$, which is the required square root.

Note: It is to be remembered that this method is the prime factorization method where we write the terms in terms of prime factors. The numbers $2$ and $7$ are prime numbers which cannot be divided any further. If there are more than $1$ pairs present in the square root, then both the numbers should be taken out of the square root and multiplied.