\(\color{white}{=}\dfrac{\sqrt{2(10-5\sqrt{2})}}{\sqrt{10+5\sqrt{2}}}\\
=\sqrt{\dfrac{2(10-5\sqrt{2})}{10+5\sqrt{2}}} \\
=\sqrt{\dfrac{10(2-\sqrt{2})} {5(2+\sqrt{2})}}\\
=\sqrt{2\dfrac{2-\sqrt{2}} {2+\sqrt{2}}}\\
=\sqrt{2\dfrac{\sqrt{2}-1}{\sqrt{2}+1}}\\
= \sqrt{2\dfrac{(\sqrt{2}-1)(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}}\\
= \sqrt{2(\sqrt{2}-1)(\sqrt{2}-1)}\)
usw...
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