Question

How does one simplify $\dfrac{{24}}{{\sqrt 3 }}$ ?

Answer 1

Hint: For solving this particular question , we have to rationalize the given number denominator by respective number, then simplify the expression by using algebraic identities and by performing arithmetic operations such as addition , subtraction , multiplication, and division . We have to convert numbers into its equivalent exponential form where required.

Formula used:In this particular question we used an identity that is ,
${a^m} \times {a^n} = {a^{m + n}}$ , exponent gets added when we have the same base.

Complete step-by-step solution:
We have to simplify the given expression that is $\dfrac{{24}}{{\sqrt 3 }}$. Now, to rationalize the denominator of the given number by multiplying and divide the given number by $\sqrt 3 $ , we have to rationalize the given number denominator by its respective conjugate. The process of multiplying and dividing by the conjugate is a useful technique , this will make the expression simpler.
We will get the following ,
$ \Rightarrow \dfrac{{24}}{{\sqrt 3 }} \times \dfrac{{\sqrt 3 }}{{\sqrt 3 }}$
Now by using algebraic identity that is , ${a^m} \times {a^n} = {a^{m + n}}$ , We will get the following ,
$ \Rightarrow \dfrac{{24\sqrt 3 }}{3}$
Simplify the above expression by performing valid arithmetic operation ,
$ \Rightarrow 8\sqrt 3 $
In exact form
$ \Rightarrow 8\sqrt 3 $
In decimal form
$ \Rightarrow 13.85640646$
Here, we get the required answer .

Hence the correct answer is $13.85640646$

Note: While rationalizing the given number denominator , you have to make sure that the resulting product must be the simpler one. Here we have to multiply and divide the number by its respective conjugate and this is a useful technique that comes up in mathematics. We have to be careful while adding the exponents of the numbers having the same base.