$\frac{\sqrt{8+\sqrt{28}}+\sqrt{8-\sqrt{28}}}{\sqrt{8+\sqrt{28}}-\sqrt{8-\sqrt{28}}}$ is equal to

If $x = \sqrt{7 + 4\sqrt{3}}$,then $x + \frac{1}{x} = ......$

Suppose $p, q, r$ are positive rational numbers such that $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is also rational. Then

For $x \ne 0$,the value of ${\left( {\frac{{{x^l}}}{{{x^m}}}} \right)^{({l^2} + lm + {m^2})}} {\left( {\frac{{{x^m}}}{{{x^n}}}} \right)^{({m^2} + nm + {n^2})}} {\left( {\frac{{{x^n}}}{{{x^l}}}} \right)^{({n^2} + nl + {l^2})}}$ is:

If ${x^{x\sqrt[3]{x}}} = {(x \cdot \sqrt[3]{x})^x}$,then $x =$

$\frac{4}{{1 + \sqrt 2 - \sqrt 3 }} = $