Question

racionalize o denominador   
a)

5√5
------
2√15

Answer 1

$\dfrac{5\sqrt{5}}{2\sqrt{15}}\\\\\\ =\dfrac{5\sqrt{5}}{2\sqrt{15}}\cdot \dfrac{\sqrt{15}}{\sqrt{15}}\\\\\\ =\dfrac{5\sqrt{5}\cdot \sqrt{15}}{2\sqrt{15}\cdot \sqrt{15}}\\\\\\ =\dfrac{5\sqrt{5\cdot 15}}{2\cdot \big(\sqrt{15}\big)^{\!\!2}}\\\\\\ =\dfrac{5\sqrt{5\cdot (5\cdot 3)}}{2\cdot 15}\\\\\\ =\dfrac{5\sqrt{5^2\cdot 3}}{2\cdot (3\cdot 5)}\\\\\\ =\dfrac{\diagup\!\!\!\! 5\cdot 5\sqrt{3}}{2\cdot 3\cdot \diagup\!\!\!\! 5}\\\\\\ =\boxed{\begin{array}{c}\dfrac{5\sqrt{3}}{6} \end{array}}$


Bons estudos! :-)