Answer

Verified

348.9k+ views

**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 the 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 {} $ is used to denote square root and this symbol of square roots is also known as radical.

**Complete step-by-step answer**:

Here we have to find the value of $ 4\sqrt {27} - \sqrt {75} $ , since both are non perfect squares so we will factorise it under the root: $ \sqrt {27} $ can be written as $ 9 \times 3 $ and we know that $ 9 $ is a perfect square and we can take out of the radical so we get,

$ \sqrt {{3^2}} \times \sqrt 3 $ $ = 3\sqrt 3 $ .

Similarly $ \sqrt {75} $ can be further written as

$ \sqrt {75} \Rightarrow {5^2} \times 3 $ , It gives $ \sqrt {{5^2}} .\sqrt 3 \Rightarrow 5\sqrt 3 $ .

By putting the values together we have:

$ 4\sqrt {27} - \sqrt {75} = 4 \times 3\sqrt 3 - 5\sqrt 3 $ .

On multiplying we have $ 12\sqrt 3 - 5\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.

Recently Updated Pages

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

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

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

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE