Answer

Verified

366.6k+ views

**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.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

A group of fish is known as class 7 english CBSE

The highest dam in India is A Bhakra dam B Tehri dam class 10 social science CBSE

Write all prime numbers between 80 and 100 class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Onam is the main festival of which state A Karnataka class 7 social science CBSE

Who administers the oath of office to the President class 10 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Kolkata port is situated on the banks of river A Ganga class 9 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE