How to divide fractions with square roots in the numerator

Asked by admin @ 05/11/2021 in Mathematics viewed by 326 People

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

Answered by admin @ 05/11/2021

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 $k=\sqrt{3}$

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