Question

Rationalize the denominator of the following-
If $\dfrac{2}{{3\sqrt 3 }}$ is $\dfrac{2}{9}\sqrt m $, then m is

Answer 1

Hint: In this particular type of question we have to rationalize the given number to eliminate the radical and compare it with the given answer to get the desired value of m.

Complete step-by-step answer:
To rationalize we have to multiply and divide the complete number by $\sqrt 3 $
$ \Rightarrow \dfrac{2}{{3\sqrt 3 }} \times \dfrac{{\sqrt 3 }}{{\sqrt 3 }} = \dfrac{{2\sqrt 3 }}{{3 \times 3}} = \dfrac{{2\sqrt 3 }}{9}$
On comparing , we get $\sqrt m = \sqrt 3$
On squaring both the side, we get m=3
So this is our required answer.

Note: Remember that root rationalization is a process by which radicals in the denominator of an algebraic fraction are eliminated . Note that this technique may be extended to any algebraic denominator, by multiplying the numerator and the denominator by all algebraic conjugates of the denominator.