Question

Racionalize os denominadores.
a) √7 √3 =

b) 4√3 √8 =

c) 10 5√2 =

d) 5√3 √6 = ​

Answer 1

$\Large\boxed{\begin{array}{l}\tt a)~\sf\dfrac{\sqrt{7}}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}=\dfrac{\sqrt{21}}{3}\\\\\tt b)~\sf\dfrac{4\sqrt{3}}{\sqrt{8}}=\dfrac{4\sqrt{3}}{2\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}\\\\\sf\dfrac{4\sqrt{6}}{2\sqrt{2^2}}=\dfrac{4\sqrt{6}}{2\cdot2}=\dfrac{\backslash\!\!\!\!4\sqrt{6}}{\backslash\!\!\!4}=\sqrt{6}\blue{\checkmark}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt c)~\sf\dfrac{10}{5\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{10\sqrt{2}}{5\sqrt{2^2}}=\dfrac{10\sqrt{2}}{5\cdot2}\\\\\sf\dfrac{\diagdown\!\!\!\!\!\!10\sqrt{2}}{\diagdown\!\!\!\!\!\!10}=\sqrt{2}\\\\\tt d)~\sf\dfrac{5\sqrt{3}}{\sqrt{6}}=\dfrac{5\,\backslash\!\!\!\!\!\sqrt{3}}{\backslash\!\!\!\!\sqrt{3}\cdot\sqrt{2}}=\dfrac{5}{\sqrt{2}}\\\\\sf\dfrac{5}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{5\sqrt{2}}{\sqrt{2^2}}=\dfrac{5\sqrt{2}}{2}\end{array}}$