Question

RACIONALIZE OS DENOMINADORES DAS FRACOES :

A) 1
\sqrt{5}

B) 30
\sqrt{15}

C) 7
3 \sqrt{21}

D) 6+ \sqrt{3}
\sqrt{3}
E) 2
3+ \sqrt{5}

Answer 1

$a) \\ \\ \dfrac{1}{ \sqrt{5} } \\ \\ \\ \dfrac{1* \sqrt{5}}{ \sqrt{5} * \sqrt{5} } \\ \\ \\ \dfrac{\sqrt{5}}{(\sqrt{5})^2} \\ \\ \\ => \dfrac{\sqrt{5}}{5}$

=====
$b) \\ \\ \dfrac{30}{\sqrt{15}} \\ \\ \\ \dfrac{30\sqrt{15}}{(\sqrt{15})*(\sqrt{15})} \\ \\ \\ \dfrac{30\sqrt{15}}{(\sqrt{15})^2} \\ \\ \\ \dfrac{30\sqrt{15}}{15}} \\ \\ \\ => 2 \sqrt{15}$

=====
$c) \\ \\ \dfrac{7}{3\sqrt{21}} \\ \\ \\ \dfrac{7 * 3\sqrt{21}}{3\sqrt{21} * 3\sqrt{21}} \\ \\ \\ \dfrac{21\sqrt{21}}{9*(\sqrt{21})^2}} \\ \\ \\ \dfrac{\not 21\sqrt{21}}{9*\not21}} \\ \\ \\ \dfrac{\sqrt{21}}{9}}$

=====
$d) \\ \\ \dfrac{6+\sqrt{3}}{ \sqrt{3}}} \\ \\ \\ \dfrac{(6+\sqrt{3}) * \sqrt{3}}{ \sqrt{3} * \sqrt{3}}} \\ \\ \\ \dfrac{3+6\sqrt{3}}{3} \\ \\ \\ => 1 + 2 \sqrt{3}$

======
$e) \\ \\ \dfrac{2}{ 3+\sqrt{5}} \\ \\ \\ \dfrac{2 * (3+\sqrt{5})}{ (3+\sqrt{5}) * (3+\sqrt{5})} \\ \\ \\ \dfrac{6+2\sqrt{5}}{14+6\sqrt{5}} \\ \\ \\ => \dfrac{3- \sqrt{5}}{2}$