Question

What is the square root of 204?

Answer 1

Hint: To find the square root of we will use the prime factorization method. Starting with the smallest prime number we represent the number 204 as a product of prime factors such as when we multiplied the numbers we will get back the same number. Then we will group the factors into groups of two and get the desired answer.

Complete step by step solution:
We have been given a number 204.
We have to find the square root of 204.
Now, we know that the square root of a number is a value when multiplied by itself given the original number back. To find the square root of 204 we will use the prime factorization method. In this method we will first represent the number 204 as a product of prime numbers.
The number 396 is represented as a product of prime factors as
\[\begin{align}
  & 2\left| \!{\underline {\,
  204 \,}} \right. \\
 & 2\left| \!{\underline {\,
  102 \,}} \right. \\
 & 3\left| \!{\underline {\,
  51 \,}} \right. \\
 & 17\left| \!{\underline {\,
  17 \,}} \right. \\
 & \text{ }\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}\]
$\Rightarrow 204=2\times 2\times 3\times 17$
Now, the square root of 204 will be
$\begin{align}
  & \Rightarrow \sqrt{204}=2\times \sqrt{3\times 17} \\
 & \Rightarrow \sqrt{204}=2\sqrt{51} \\
\end{align}$

Hence we get the square root of 204 as $2\sqrt{51}$.

Note: Prime numbers are those numbers which have only two factors i.e. the number itself and 1. Prime numbers are always greater than 1. 2 is the smallest prime number. Alternatively we can also use the long division method to find the square root of any number. But mostly we will use the long division method for big numbers.