a)
\(\sqrt{5\left(1-\sqrt{2}\right)^2}\\ =\sqrt{5}\left|1-\sqrt{2}\right|\left(1\right)\)
Mà \(1< \sqrt{2}\) nên:
(1)\(=\sqrt{5}\left(\sqrt{2}-1\right)=\sqrt{10}-\sqrt{5}\)
b)
\(\sqrt{27.\left(2-\sqrt{5}\right)^2}\\ =\sqrt{27}.\left|2-\sqrt{5}\right|\left(1\right)\)
Mà \(2< \sqrt{5}\) nên:
`(1)`=\(\sqrt{27}\left(\sqrt{5}-2\right)=3\sqrt{3}\left(\sqrt{5}-2\right)\)
\(=3\sqrt{15}-6\sqrt{3}\)
c)
\(=\dfrac{\sqrt{2}}{\left|3-\sqrt{10}\right|}=\dfrac{\sqrt{2}}{\sqrt{10}-3}\) (vì \(3< \sqrt{10}\))
\(=\dfrac{\sqrt{2}\left(\sqrt{10}+3\right)}{10-9}\\ =\sqrt{20}+3\sqrt{2}\\ =2\sqrt{5}+3\sqrt{2}\)
d)
\(=\dfrac{5\left|1-\sqrt{3}\right|}{\sqrt{4}}=\dfrac{5\left(\sqrt{3}-1\right)}{2}\) (vì \(1< \sqrt{3}\))
\(=\dfrac{5\sqrt{3}-5}{2}\)
