Question

4. Solve this question
Please give verified answer with step by step solution​

Answer 1

Answer:

Here you go.................

Answer 2

11.904

Step-by-step explanation:

Given:

√3 = 1.732

√5 = 2.236

To find:

$\dfrac{6}{\sqrt{5} - \sqrt{3}}$

Solution:

Answer in 4 step

1. Rationalizing the denominator.

2. Substitute the given value.

3. Simplify and get the answer.

$\sf\:\dfrac{6}{\sqrt{5}\:-\:\sqrt{3}}\\\\\implies\sf\:\dfrac{6(\sqrt{5}\:+\:\sqrt{3})}{\sqrt{5}\:-\:\sqrt{3})\:(\sqrt{5}\:+\:\sqrt{3})}\:\:\:[\:because\:(a+b)\:(a-b)\:=\:a^{2}\:-\:b^{2}\:]\\\\\implies\sf\:\dfrac{6\sqrt{5}\:+\:\sqrt{3}}{(\sqrt{5})^{2}\:-\:(\sqrt{3})^{2}}\\\\\implies\sf\:\dfrac{6(\sqrt{5}\:+\:3}{5-3}\\\\\implies\sf\:\dfrac{6(\sqrt{5}\:+\:\sqrt{3})}{2}\\\\\implies\sf\:3\:(\sqrt{5}\:+\:\sqrt{3}$

Now, Putting the value of √5 and √3

$= 3(2.236 + 1.732) \\ \\ = 3(3.968) \\ \\ = 3 \times 3.968 \\ \\ = 11.904$

Therefore, the required answer is 11.904