√8√3 + 2√25√12 - 4√192
= √2.√4.√3 + 2.5.√4.√3 - 4.√16.√4.√3
= 2√6 + 10.√12 - 16.√12
= 2√6 - 6√12
= 2√6 - 6.√4.√3
= 2√6 - 6.2.√3
= 2√6 - 12√3

\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}=\frac{\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}}{\sqrt{2}}=\frac{\sqrt{5-2\sqrt{5}+1}+\sqrt{5+2\sqrt{5}+1}}{\sqrt{2}}=\frac{\sqrt{\left(\sqrt{5}-1\right)^2}+\sqrt{\left(\sqrt{5}+1\right)^2}}{\sqrt{2}}=\frac{\sqrt{5}-1+\sqrt{5}+1}{\sqrt{2}}=\frac{2\sqrt{5}}{\sqrt{2}}=\sqrt{10}\)

chúc bạn học tốt:)

\(\sqrt{2}\sqrt{4}\sqrt{3}+2.5\sqrt{4}\sqrt{3}-4\sqrt{16}\sqrt{4}\sqrt{3}=2\sqrt{6}+10\sqrt{12}-16\sqrt{12}=2\sqrt{6}-6\sqrt{12}=2\sqrt{6}-12\sqrt{3}\)
 

Sao cậu không bấm máy tính?

h)\(\sqrt{5}+\sqrt{9-4\sqrt{5}}=\sqrt{5}+\sqrt{\left(\sqrt{5}\right)^2-2.2.\sqrt{5}+2^2}\)

\(=\sqrt{5}+\sqrt{\left(\sqrt{5-2}\right)^2}\)

\(=\sqrt{5}+\left|\sqrt{5}-2\right|\)

\(=\sqrt{5}+\sqrt{5}-2\)

\(=2\sqrt{5}-2\)

i. \(2\sqrt{2\sqrt{3}}-10\sqrt{2\sqrt{3}}+8\sqrt{2\sqrt{3}}=\sqrt{2\sqrt{3}}\left(2-10+8\right)\)

\(=\sqrt{2\sqrt{3}}.0=0\)

\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}=0\)

b: \(=\dfrac{\sqrt{20}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{5}+\sqrt{2}}-\dfrac{8}{\sqrt{5}-1}\)

\(=2\sqrt{5}-2-2\sqrt{5}\)

=-2

c: \(=\dfrac{\sqrt{4}\left(2\sqrt{2}-\sqrt{3}\right)}{\sqrt{6}\left(\sqrt{3}-2\sqrt{2}\right)}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{6}\left(\sqrt{5}+\sqrt{27}\right)}\)

\(=\dfrac{-3}{\sqrt{6}}=-\dfrac{\sqrt{6}}{2}\)