\(\begin{array}{l}
28)\quad \sqrt{2 - \sqrt3}.\left(\sqrt6 + \sqrt2\right)\\
= \sqrt{2 - \sqrt3}.\sqrt2\left(\sqrt3 + 1\right)\\
= \sqrt{4 - 2\sqrt3}.\left(\sqrt3 + 1\right)\\
= \sqrt{\left(\sqrt3\right)^2 - 2.\sqrt3.1}.\left(\sqrt3 + 1\right)\\
= \sqrt{\left(\sqrt3 - 1\right)^2}.\left(\sqrt3 + 1\right)\\
= \left(\sqrt3 - 1\right).\left(\sqrt3 + 1\right)\\
= \left(\sqrt3\right)^2 - 1^2\\
= 3 - 1\\
= 2\\
29)\quad \sqrt{4 + \sqrt{6 - 2\sqrt5}}\\
= \sqrt{4 + \sqrt{\left(\sqrt5\right)^2- 2.\sqrt5.1 + 1^2}}\\
= \sqrt{4 + \sqrt{\left(\sqrt5 - 1\right)^2}}\\
= \sqrt{4 + \left(\sqrt5 - 1\right)}\\
= \sqrt{3 + \sqrt5}\\
= \sqrt{\dfrac{6 + 2\sqrt5}{2}}\\
= \sqrt{\dfrac{\left(\sqrt5\right)^2 + 2.\sqrt5.1 + 1^2}{2}}\\
= \sqrt{\dfrac{\left(\sqrt5 + 1\right)^2}{2}}\\
= \dfrac{\sqrt5 + 1}{\sqrt2}\\
= \dfrac{\sqrt{10} + \sqrt2}{2}\\
30)\quad \left(\sqrt{21} + 7\right)\sqrt{10 - 2\sqrt{21}}\\
= \left(\sqrt{21} + 7\right)\sqrt{\left(\sqrt7\right)^2 - 2.\sqrt7.\sqrt3 + \left(\sqrt3\right)^2}\\
= \left(\sqrt{21} + 7\right)\sqrt{\left(\sqrt7 - \sqrt3\right)^2}\\
= \sqrt7\left(\sqrt{3} + \sqrt7\right)\left(\sqrt7 - \sqrt3\right)\\
= \sqrt7\left[\left(\sqrt7\right)^2 - \left(\sqrt3\right)^2\right]\\
= \sqrt7(7 - 3)\\
= 4\sqrt7\\
31)\quad \left(7 + \sqrt{14}\right)\sqrt{9 - 2\sqrt{14}}\\
= \left(7 + \sqrt{14}\right)\sqrt{\left(\sqrt7\right)^2 - 2.\sqrt7.\sqrt2 + \left(\sqrt2\right)^2}\\
= \left(7 + \sqrt{14}\right)\sqrt{\left(\sqrt7 - \sqrt2\right)^2}\\
= \sqrt7\left(\sqrt7 + \sqrt2\right)\left(\sqrt7 - \sqrt2\right)\\
= \sqrt7\left[\left(\sqrt7\right)^2 - \left(\sqrt2\right)^2\right]\\
= \sqrt7(7 - 2)\\
= 5\sqrt7
\end{array}\)
