Chapter 0.9, Problem 16E

To determine

To simplify the given expression

Answer to Problem 16E

  $\frac{35\sqrt{3}+42\sqrt{2}}{13}$

Explanation of Solution

Given information:

  $\frac{7\sqrt{3}}{5-2\sqrt{6}}$

Calculation:

Factorizing,

  $\frac{7\sqrt{3}}{5-2\sqrt{6}}\times \frac{5+2\sqrt{6}}{5+2\sqrt{6}}$

So,

  $\frac{7\sqrt{3}(5+2\sqrt{6})}{{(5)}^2-{(2\sqrt{6})}^2}$ _____________________(using, $(a-b)(a+b)=a^2-b^2$ )

So,

  $\frac{35\sqrt{3}+42\sqrt{2}}{25-12}$

On solving,

  $\frac{35\sqrt{3}+42\sqrt{2}}{13}$