Question

How do you simplify $\sqrt {363} $?

Answer 1

Hint:The above question is based on the concept of square root of a number. The main approach towards solving the equation is to reduce the number 363 into its factors and then further taking common terms

Complete step by step solution:
Square root of a number is a number which is multiplied by itself to give the original number. Now suppose for example if a is the square root of b and it is represented as \[a = \sqrt b \] and also it can be written as \[{a^2} = b\]. Here the square root sign is called a radical sign. For example, the square of 2 is 4, therefore the square root of 4 is 2.
The above given number is $\sqrt {363} $
The above given number is not a perfect square it is an imperfect square .So now will first check the factors of the number 363.It can have factors like 121 and 3.
\[363 = 121 \times 3\]
121 can be further divided into 11 multiplied by 11. So it can be written as
\[363 = {11^2} \times 3\]
\[\sqrt {363} = \sqrt {{{11}^2} \times 3} \]
So the square root of 11 multiplied by 11 is a single number 11 since it is a square. Therefore, we can write it has
\[\sqrt {363} = \sqrt {{{11}^2}} \times \sqrt 3 = 11\sqrt 3 \]
So, we get the square root of 363 as above value which is \[11\sqrt 3 \].

Note: An important thing to note is that the value is the root form; it can further be simplified by writing it in decimal form. The value of \[\sqrt 3 \] is 1.732 so on further multiplying the value of 1.73 with the number 11 we get the decimal value as 19.052.