Question

√5-√13+4√3 + √3+13+4√3

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Answer 1

\(\sqrt{5-\sqrt{13+4\sqrt{3}+\sqrt{3+\sqrt{13+4\sqrt{3}}}}}\)

\(=\sqrt{5-\sqrt{13+4\sqrt{3}+\sqrt{3}+1}}\)

\(=\sqrt{5-\sqrt{14+5\sqrt{3}}}\)

\(=\dfrac{\sqrt{10-2\sqrt{14+5\sqrt{3}}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{10-\sqrt{2}\cdot\left(\sqrt{5}+3\right)}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{10-\sqrt{10}-3\sqrt{2}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{20-2\sqrt{10}-6\sqrt{2}}}{2}\)

Answer 2

\(\sqrt{5}-\sqrt{13}+4\sqrt{3}+\sqrt{3}+4\sqrt{3}+13\)

=27.21897397