Chapter 1.1, Problem 73SPR

To determine

To simplify the given equation

Answer to Problem 73SPR

  $-8\sqrt{3}+4\sqrt{15}$

Explanation of Solution

Given information:

  $\frac{4\sqrt{3}}{2+\sqrt{5}}$

Formula used:

Factorization

Calculation:

On factorizing,

  $\frac{4\sqrt{3}}{2+\sqrt{5}}\times \frac{2-\sqrt{5}}{2-\sqrt{5}}$

On solving,

  $\frac{4\sqrt{3}(2-\sqrt{5})}{{(2)}^2-{(\sqrt{5})}^2}$ _______________________ (using $(a+b)(a-b)=a^2-b^2$ )

On solving,

  $\frac{8\sqrt{3}-4\sqrt{15}}{4-5}$

So,

  $\frac{8\sqrt{3}-4\sqrt{15}}{-1}$

On solving,

  $-8\sqrt{3}+4\sqrt{15}$

Hence, simplified.