\(a=\sqrt{5}+\sqrt{\dfrac{1}{5}}=\sqrt{5}+\dfrac{1}{\sqrt{5}}=\dfrac{5+1}{\sqrt{5}}=\dfrac{6\sqrt{5}}{5}\)
\(\sqrt{5a^2-4a\sqrt{5}+4}\)
\(=\sqrt{\left(\sqrt{5}a\right)^2-4\times\left(\sqrt{5}a\right)+4}\)
\(=\sqrt{\left(\sqrt{5}a-2\right)^2}\)
\(=\left|\sqrt{5}a-2\right|\)
\(=\left|\sqrt{5}\times\dfrac{6\sqrt{5}}{5}-2\right|\)
= 4
~ ~ ~
\(\dfrac{\sqrt{1-2m+m^2}}{m^2-1}\)
\(=\dfrac{\sqrt{\left(1-m\right)^2}}{\left(m-1\right)\left(m+1\right)}\)
\(=\dfrac{\left|1-m\right|}{\left(m-1\right)\left(m+1\right)}\)
\(=\dfrac{m-1}{\left(m-1\right)\left(m+1\right)}\) (m > 1)
\(=\dfrac{1}{m+1}\)
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