Chapter SH, Problem 7.19EP

To determine

To solve equation

  $\frac{6}{\sqrt{3}+2}$ .

Answer to Problem 7.19EP

  $12-6\sqrt{3}$

Explanation of Solution

Given information:

Expression

  $\frac{6}{\sqrt{3}+2}$

Calculation:

  $\frac{6}{\sqrt{3}+2}$

On rationalisation,

  $=\frac{6}{\sqrt{3}+2}\times \frac{\sqrt{3}-2}{\sqrt{3}-2}$

So,

  $=\frac{6(\sqrt{3}-2)}{(\sqrt{3}+2)(\sqrt{3}-2)}$

Using identity

  $(a+b)(a-b)=a^2-b^2$

  $=\frac{6(\sqrt{3}-2)}{{(\sqrt{3})}^2-2^2}$

On solving,

  $=\frac{6(\sqrt{3}-2)}{3-4}$

On solving,

  $=\frac{6(\sqrt{3}-2)}{-1}$

On solving,

  $=12-6\sqrt{3}$

Hence, final anwers is $12-6\sqrt{3}$