Question

alguém me ajuda ja fiz de tudo mais ñ consegui fazer

racionalize os denominadores das seguintes questões

a)
$\frac{3 \sqrt{2} }{5 \sqrt{6} }$
b)
$\frac{5 \sqrt{2} }{2 \sqrt{5} }$
c)
$\frac{7 \sqrt{6} }{3 \sqrt{2} }$


​

Answer 1

$\boxed{\begin{array}{l}\tt a)\sf\dfrac{3\sqrt{2}}{5\sqrt{6}}=\dfrac{3\sqrt{2}\cdot\sqrt{6}}{5\cdot6}\\\sf=\dfrac{\diagup\!\!\!3\cdot\diagup\!\!\!2\sqrt{3}}{5\cdot\diagup\!\!\!3\cdot\diagup\!\!\!2}=\dfrac{\sqrt{3}}{5}\\\tt b)~\sf\dfrac{5\sqrt{2}}{2\sqrt{5}}=\dfrac{\diagup\!\!\!5\sqrt{2}\cdot\sqrt{5}}{2\cdot\diagup\!\!\!5}=\dfrac{\sqrt{10}}{2}\\\tt c)~\sf\dfrac{7\sqrt{6}}{3\sqrt{2}}=\dfrac{7\sqrt{6}\cdot\sqrt{2}}{3\cdot2}\\\sf\dfrac{7\cdot\diagup\!\!\!2\sqrt{3}}{3\cdot\diagup\!\!\!2}=\dfrac{7\sqrt{3}}{3}\end{array}}\blue{\checkmark}$