Question

rationalize the denominator of the following expression and simplify: 5 + sqrt 3/ 2 - sqrt 3

Answer 1

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

multiply by the conjugate of the denominator

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

using the rule:

$(a+b)(a-b)=a^2-b^2$

then,

$\frac{5+\sqrt{3}}{2-\sqrt{3}}\times\frac{2+\sqrt{3}}{2+\sqrt{3}}=\frac{(5+\sqrt{3})(2+\sqrt{3})}{2^2-(\sqrt{3})^2}$

simplify

$\begin{gathered} \frac{10+5\sqrt{3}+2\sqrt{3}+(\sqrt{3})^2}{4-3} \\ \frac{10+5\sqrt{3}+2\sqrt{3}+3}{1} \\ 13+7\sqrt{3} \end{gathered}$

Answer:

After rationalizing the denominator the simplified expression is:

$13+7\sqrt{3}$