Question

\(\sqrt{5\sqrt{3}+5\sqrt{48}-10\sqrt{7+4\sqrt{3}}}\)

\(\sqrt{4+\sqrt{10}+2\sqrt{5}}+\sqrt{4-\sqrt{10}+2\sqrt{5}}\)

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Answer 1

b/ \(B=\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)

\(\Leftrightarrow B^2=8+2\sqrt{4+\sqrt{10+2\sqrt{5}}}.\sqrt{4-\sqrt{10+2\sqrt{5}}}\)

\(=8+2\sqrt{6-2\sqrt{5}}\)

\(=8+2\sqrt{\left(\sqrt{5}-1\right)^2}\)

\(=6+2\sqrt{5}=\left(\sqrt{5}+1\right)^2\)

\(\Rightarrow B=\sqrt{5}+1\)

Answer 2

a/ \(\sqrt{5\sqrt{3}+5\sqrt{48}-10\sqrt{7+4\sqrt{3}}}\)

\(=\sqrt{5\sqrt{3}+20\sqrt{3}-10\sqrt{\left(2+\sqrt{3}\right)^2}}\)

\(=\sqrt{5\sqrt{3}+20\sqrt{3}-20-10\sqrt{3}}\)

\(=\sqrt{15\sqrt{3}-20}\)