How do I simplify square root $ 48 $ $ + $ square root $ 27? $

Hint: As we know that square root can be defined as a number which when multiplied by itself gives a number as the product. For example $ 5 \times 5 = 25 $ , here square root of $ 25 $ is $ 5 $ . There is no such formula to calculate square root formula but two ways are generally considered. They are the prime factorization method and division method. The symbol $ \sqrt {\text{ }} $ is used to denote square roots and this symbol of square roots is also known as radical.

Complete step by step solution:
Here we have to find the value of $ \sqrt {48} + \sqrt {27} $ , since both are non perfect squares so we will factorise it under the root: $ \sqrt {48} $ can be written as $ {4^2} \times 2 $ and we know that $ 4 $ is a perfect square and we can take out of the radical so we get, $ \sqrt {{4^2}} \times \sqrt 3 $
$ = 4\sqrt 3 $ .
Similarly $ \sqrt {27} $ can be further written as $ \sqrt {27} \Rightarrow {3^2} \times 3 $ , It gives $ \sqrt {{3^2}} .\sqrt 3 \Rightarrow 3\sqrt 3 $ .
By putting the values together we have: $ \sqrt {48} + \sqrt {27} = 4\sqrt 3 + 3\sqrt 3 $ . It gives the value $ 7\sqrt 3 $
Hence the answer is $ 7\sqrt 3 . $ .
So, the correct answer is “ $ 7\sqrt 3 . $ ”.

Note: The above given numbers are non-perfect squares as we know that a non-perfect square is a number that there is no rational number i.e. it is considered as an irrational number. Their decimal does not end and they do not repeat a pattern so they are also non-terminating and non-repeating numbers. The number written inside the square root symbol or radical is known as radicand. We know that all real numbers have two square roots, one is a positive square root and another one is a negative square root. The positive square root is also referred to as the principal square root.