Question

how do you simplify the \[\dfrac{2}{{\sqrt 3 }}\]?

Answer 1

Hint: In the above question we are given an expression that is \[\dfrac{2}{{\sqrt 3 }}\] which is a radical expression with a square root in its denominator. So while approaching such kind of questions one should know about the radical expression and the square root of the expression as the radical expression are the those expressions which contain the square root , cube root or fractional form in their expressions and the square root of an expression is the number which when squared produces the same expression. In this question the square root is present in the denominator we would first eliminate that and will further do the simplification of the expression. Now let us see the simplification of the given term\[\dfrac{2}{{\sqrt 3 }}\] in the complete step by step solution.

Complete step by step solution:
Here we are given a term that is\[\dfrac{2}{{\sqrt 3 }}\] and we are asked to simplify it.
So firstly by seeing the expression given we can say that it is a radical expression (the expressions which contain the square root, cube root or fractional form in their expressions) and it has square root in its denominator also which means we need to eliminate this that would be done with the help of the multiplying the numerator with the number present in the denominator that is \[\sqrt 3 \] and later we would do the further simplification to get the desired answer. So the simplification of the given term \[\dfrac{2}{{\sqrt 3 }}\] is done as-
We are given term that is \[\dfrac{2}{{\sqrt 3 }}\] we would first multiply the both numerator and the denominator with the \[\sqrt 3 \] to eliminate the square root present in the denominator that is –
\[
  \dfrac{2}{{\sqrt 3 }} \times \dfrac{{\sqrt 3 }}{{\sqrt 3 }} \\
   = \dfrac{{2\sqrt 3 }}{3} \\
 \]
Now we can either leave it here as the answer would become \[ = \dfrac{{2\sqrt 3 }}{3}\]or we can further solve it by putting the values of \[\sqrt 3 \]that is\[1.73\] in the resultant fraction \[ = \dfrac{{2\sqrt 3 }}{3}\]and the finding the answer in the decimal form that is depicted below –
\[
   = \dfrac{{2 \times 1.73}}{3} \\
   = \dfrac{{3.46}}{3} \\
   = 1.153 \\
 \]
So the decimal answer form is \[ 1.1533\] which shows it’s a non-terminating decimal (those decimals in which the number after the decimal keeps on increasing that is also stated as when the fraction is solved it does not terminate).

Note:
While solving this kind of question one should know about the radical expression and the method to solve them as in this the square root is in the denominator that we have terminated with the help of multiplying the number with both numerator and the denominator. Also the answer can be left out in the fractional form or in the decimal form if a certain form is not stated in the question and the utter concentration which would lead to the precision in the solution and getting the right answer also.