Question

How do you simplify $ \dfrac{6}{{\sqrt 3 }} $ ?

Answer 1

Hint: In the given fraction denominator having a irrational number, to simplify the fraction first we rationalise the denominator in the fraction that is eliminate radical from the denominator to do this multiply the numerator and denominator by $ \sqrt 3 $ then by simplification we get the required result

Complete step-by-step answer:
The given question in the form of $ \dfrac{a}{b} $ where, a is the numerator and b is the denominator this form is known as fraction, there are mainly two types of fraction namely
Proper fraction: If the numerator is smaller than the denominator is known as proper fraction.

Improper fraction: If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction.

Simplification of fraction means reduce the given fraction to the simplest form.
Here in this question, we have to simplify the given fraction $ \dfrac{6}{{\sqrt 3 }} $
As most of all times in mathematics, we don’t want a square root in the denominator. In order to get it out, multiply the fraction by another fraction, and that other fraction is the square root over itself.
Consider the fraction
 $ \Rightarrow \,\,\dfrac{6}{{\sqrt 3 }} $
Multiply the another fraction both numerator and denominator having $ \sqrt 3 $ , by doing this we actually are not changing the value of the given fraction, since the value of $ \dfrac{{\sqrt 3 }}{{\sqrt 3 }} $ equals 1 .
 $ \Rightarrow \,\,\dfrac{6}{{\sqrt 3 }} \times \dfrac{{\sqrt 3 }}{{\sqrt 3 }} $
 $ \Rightarrow \dfrac{{6\sqrt 3 }}{{\sqrt 3 .\sqrt 3 }} $
 $ \Rightarrow \dfrac{{6\sqrt 3 }}{{{{\left( {\sqrt 3 } \right)}^2}}} $ []
 $ \Rightarrow \dfrac{{6\sqrt 3 }}{3} $
 $ \therefore \,\,\,\dfrac{6}{{\sqrt 3 }} = 2\sqrt 3 $
Hence, the value of the given fraction $ \dfrac{6}{{\sqrt 3 }} $ is $ 2\sqrt 3 $ .
So, the correct answer is “ $ 2\sqrt 3 $”.

Note: If the question involves the root, especially square root, we rationalise the number. We can rationalise the numerator and also denominator. By rationalising we get a real number and we can simplify the number with the help of simply division. For the division and multiplication we need tables of multiplication.