Question

When the denominator of \dfrac{2}{\sqrt{3}} 3 ​ 2 ​ start fraction, 2, divided by, square root of, 3, end square root, end fraction is rationalized, it becomes \dfrac{2k}{3} 3 2k ​ start fraction, 2, k, divided by, 3, end fraction. Find kkk

Answer 1

Answer:

$k=\sqrt{3}$

Step-by-step explanation:

Given:

On rationalizing the denominator of $\frac{2}{\sqrt{3}}$ we get $\frac{2k}{3}$.

To find value of $k$.

Solution.

In order to rationalize a radical denominator we will multiply the numerator and denominator with the radical as multiplying same numbers to numerator and denominator does not effect the proportions. This will remove the radical from the denominator.

For the given fraction with radical 3 in denominator, we will rationalize by multiplying numerator and denominator with radical 3.

So, we have

$\frac{2}{\sqrt{3}}$

Rationalizing.

⇒ $\frac{2\times\sqrt{3}}{\sqrt{3}\times\sqrt{3}}$

⇒ $\frac{2\times\sqrt{3}}{(\sqrt{3})^2}$

We get,

$\frac{2\sqrt{3}}{3}$

On comparing it with the result given which is $\frac{2k}{3}$

we find out that value of $k=\sqrt{3}$