Question

How do you simplify the square root of $18$?

Answer 1

Hint: A positive integer, when multiplied by itself gives the square of a number. The square root of the square of an integer gives the original number. To find the square root of $18$ , we simply need to factorize the given number inside the square root and then take out the repeating number and write it once outside the square root.

Complete step-by-step solution:
In order to simplify the square root of $18$, first of all factorize $18$.
Factors of $18 = 2 \times 3 \times 3$
\[ \Rightarrow \sqrt {18} = \sqrt {2 \times 3 \times 3} \]
Here, 3 is repeated 2 times, so we write it as ${\left( 3 \right)^2}$ inside the square root.
$ \Rightarrow \sqrt {18} = \sqrt {2 \times {{\left( 3 \right)}^2}} $
Now, we know that we can cancel square and square root and we can take the term out of square root.
$ \Rightarrow \sqrt {18} = 3\sqrt 2 $
This is the final form and our final answer.
We can also write it in decimal form by writing the value of $\sqrt 2 $.
We know that the value of $\sqrt 2 $ is $1.414$. So, by multiplying it with 3, we get our answer in decimal form.
$
   \Rightarrow \sqrt {18} = 3 \times 1.414 \\
   \Rightarrow \sqrt {18} = 4.242 \\
 $
Hence, the simplified form of$\sqrt {18} $ is $3\sqrt 2 $ and the decimal form is $4.242$.

Note: Here, the symbol $'\sqrt {} '$ is called Radical and the number inside the symbol is called radicand.
Square root of any number is calculated by prime factoring the given number inside the square root itself.
Prime factorization means expressing the number in the form of a product of the prime numbers used to construct the number.