Answer

Verified

384k+ views

**Hint:**Here, we are asked to simplify the fraction whose denominator is a square root value. Thus, ultimately we have to rationalize the denominator in this question. Rationalization is defined as the process of removing the radical or imaginary number from the denominator of a fraction. Generally, the denominator of a fraction can be rationalized by taking the conjugate of a denominator and multiplying it by both the numerator and denominator.

**Complete step-by-step solution:**

We are given the value $\dfrac{1}{{\sqrt 3 }}$.

We will now rationalize its denominator. We will do it by removing $\sqrt 3 $from the denominator, and replace it with a whole number.

For this we will divide and multiply the given number with $\sqrt 3 $.

$ \Rightarrow \dfrac{1}{{\sqrt 3 }} \times \dfrac{{\sqrt 3 }}{{\sqrt 3 }} = \dfrac{{\sqrt 3 }}{{\sqrt 3 \times \sqrt 3 }}$

We know that when a number is multiplied two time by itself then it will give the square of the number.

Therefore, here in the denominator, $\sqrt 3 $ is multiplied with $\sqrt 3 $which will give us its square value which is 3. This means that $\sqrt 3 \times \sqrt 3 = 3$.

Thus, we can write

$ \Rightarrow \dfrac{1}{{\sqrt 3 }} \times \dfrac{{\sqrt 3 }}{{\sqrt 3 }} = \dfrac{{\sqrt 3 }}{{\sqrt 3 \times \sqrt 3 }} = \dfrac{{\sqrt 3 }}{3}$

Thus, by simplifying $\dfrac{1}{{\sqrt 3 }}$, we get $\dfrac{{\sqrt 3 }}{3}$.

**Note:**Here, we have done nothing but converted the denominator into the whole number. It does not mean that it is wrong to write $\dfrac{1}{{\sqrt 3 }}$but it is the standard form is to avoid roots in denominators, if possible. Moreover, rationalizing the denominator is a useful skill that can help us to solve problems in higher mathematics. For example, in calculus, it is a trick that can often help us to solve some problems about limits as well as complex numbers.

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

Guru Purnima speech in English in 100 words class 7 english CBSE

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

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Difference Between Plant Cell and Animal Cell

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

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

Give 10 examples for herbs , shrubs , climbers , creepers