Question

$(\sqrt[4]{3} - \sqrt[4]{27})^{2} \div (6 - 4 \sqrt{3} )$

Answer 1

$(\sqrt[4]{3} - \sqrt[4]{27})^{2}:(6 - 4 \sqrt{3} )=$

$\frac{(3^{ \frac{1}{4} }-27^{ \frac{1}{4} })^2}{6 - 4 \sqrt{3}}=$

$\frac{(3^{ \frac{1}{4} })^2-2 \cdot3^{ \frac{1}{4} } \cdot 27^{ \frac{1}{4}}+ (27^{ \frac{1}{4})^2 }}{6 - 4 \sqrt{3}}=$

$\frac{3^{ \frac{1}{2} }-2 \cdot(3 \cdot 27)^{ \frac{1}{4}}+ 27^{ \frac{1}{2}}}{6 - 4 \sqrt{3}}=$

$\frac{ \sqrt{3} -2 \cdot(81)^{ \frac{1}{4}}+ \sqrt{27}}{6 - 4 \sqrt{3}}=$

$\frac{ \sqrt{3} -2 \cdot3+ 3 \sqrt{3}}{6 - 4 \sqrt{3}}=$

$\frac{-6+4 \sqrt{3}}{6 - 4 \sqrt{3}}=\frac{-(6- \sqrt{3})}{6 - 4 \sqrt{3}}=-1$