Question

Только номера, отмеченные галочкой.

Answer 1

$displaystyle 1) frac{left(3sqrt{6}right)^2}{18}=frac{3^2cdot :6}{18}=frac{3^2}{3}=3 \ \ \ 3)sqrt{3frac{6}{7}}cdot sqrt{2frac{1}{3}}=sqrt{frac{27}{7}}sqrt{2 frac{1}{3}}=sqrt{frac{27}{7}}sqrt{frac{7}{3}}=frac{3sqrt{3}}{sqrt{7}}sqrt{frac{7}{3}}=frac{3sqrt{3}sqrt{frac{7}{3}}}{sqrt{7}}=$
$=displaystyle frac{3sqrt{3}frac{sqrt{7}}{sqrt{3}}}{sqrt{7}}=frac{3sqrt{7}}{sqrt{7}}=3 \ \ \ 5)sqrt{16-sqrt{31}}sqrt{sqrt{31}+16}=sqrt{left(16sqrt{31}right)left(16+sqrt{31}right)}=$
$=6^2-left(sqrt{31}right)^2=256-31=sqrt{225}=15 \ \ \ displaystyle 7)frac{sqrt{3+sqrt{5}}}{sqrt{3-sqrt{5}}}+frac{sqrt{3-sqrt{5}}}{sqrt{3+sqrt{5}}}=sqrt{frac{3+sqrt{5}}{3-sqrt{5}}}+sqrt{frac{3-sqrt{5}}{3+sqrt{5}}}=$
$displaystyle = sqrt{frac{3sqrt{5}+7}{2}}+sqrt{frac{3-sqrt{5}}{3+sqrt{5}}}=sqrt{frac{3sqrt{5}+7}{2}}+sqrt{frac{7-3sqrt{5}}{2}}=3$

Answer 2

Спасибо.