Question

Calcule o valor das expressões

$<var> \sqrt{11\sqrt{27-\sqrt{1}+\sqrt{9}}} \\ \\ \sqrt{15}.\sqrt{40} \\ \\ (2\sqrt{50}+2\sqrt{18}-\sqrt{2}):\sqrt[4]{\sqrt[3]{2^{6}}} \\ \\ (\sqrt{27}+4\sqrt{3})-\sqrt[5]{\sqrt[4]{3^{10}}}$

 

Racionalize o denominador de cada uma das expressões a seguir.

$\\ \\ \frac{5}{\sqrt{5}}} \\ \\ \frac{2}{\sqrt{3}}} \\ \\ \frac{2}{2\sqrt{3}}} \\ \\ \frac{5}{\sqrt{6}}} </var>$

Answer 1

Alunos, boa noite. Seguem as soluções (por atacado, rsrs):

 

$=\sqrt{11-\sqrt{27-1+3}}=\sqrt{11-\sqrt{29}}$

 

 

 

$=\sqrt{3.5.2^3.5}=5.2\sqrt{3.2}=10\sqrt{6}$

 

 

 

$=(2\sqrt{2.5^2}+2\sqrt{2.3^2}-\sqrt{2}):2^\frac{6}{3.4}$
$=(10\sqrt{2}+6\sqrt{2}-\sqrt{2}):2^\frac12=$
$=15\sqrt{2}:\sqrt{2}=$
$=15$

 

 

 

$=(\sqrt{3^2.3}+4\sqrt{3})-3^\frac{10}{5.4}=$
$=(3\sqrt{3}+4\sqrt{3})-3^\frac12=$
$=7\sqrt{3}-\sqrt{3}=$
$=6\sqrt{3}$

 

 

 

$=\frac{5\sqrt{5}}{5}=\sqrt{5}$

 

 

 

$=\frac{2\sqrt{3}}{3}$

 

 

 

$=\frac{2\sqrt{3}}{2.3}=\frac{\sqrt{3}}{3}$

 

 

 

$=\frac{5\sqrt{6}}{6}$