Question

What is the simplest radical form of the square root of 216?

Answer 1

Hint: To solve the question, we need to know the concept of square root. In this question, we will prime factorize the number to find the square root of the number. We will use the Prime Factorization to get the factors of the number as it will help in finding the factors of the number easily.

Complete step-by-step answer:
The question asks us to write the value of 216 in a radical format, where “$\sqrt{x}$ ” is a radical format number. Here, the term written as “$\sqrt{x}$ ” has two meaningful terms inside it. The root sign is called the radical sign and the number ‘x’ written inside it is called the radicand. To solve our problem, the first step would be to prime factorize our number 216.
To find the square root of our number, we are writing the number as a product of its prime factors. The prime factorization of 216 can be done as follows:
$\Rightarrow 216=2\times 2\times 2\times 3\times 3\times 3$

Now, substituting 216 with the product of its prime factors, we get the following equation:
$\Rightarrow \sqrt{216}=\sqrt{2\times 2\times 2\times 3\times 3\times 3}$
Taking out the numbers which repeat twice out of the square root, we get:
$\begin{align}
  & \Rightarrow \sqrt{216}=2\times 3\sqrt{2\times 3} \\
 & \therefore \sqrt{216}=6\sqrt{6} \\
\end{align}$

Thus, we get the final resulting number as $6\sqrt{6}$.
Hence, the simplest radical form of the square root of 216 comes out to be $6\sqrt{6}$.

Note: We can always check our solution after calculating the simplest radical form of a number. This can be done by squaring the final radical form number obtained and checking if its equal to our original number. In our case, the square of $6\sqrt{6}$ comes out to be equal to 216. This verifies that our procedure and the final answer, both are correct.