Question

Answer 1

\(M=2^2+\dfrac{4\sqrt{7}-4\sqrt{5}}{\sqrt{7}-\sqrt{5}}-\sqrt{\left(2\sqrt{5}-3\right)^2}+\dfrac{220}{2\sqrt{5}\left(4+\sqrt{5}\right)}\)
\(M=4+\dfrac{4\left(\sqrt{7}-\sqrt{5}\right)}{\sqrt{7}-\sqrt{5}}-2\sqrt{5}+3+\dfrac{22\sqrt{5}}{4+\sqrt{5}}\)
\(M=4+4-2\sqrt{5}+3+\dfrac{22\sqrt{5}\left(4-\sqrt{5}\right)}{16-5}\)
\(M=11-2\sqrt{5}+2\sqrt{5}\left(4-\sqrt{5}\right)\)
\(M=11-2\sqrt{5}+8\sqrt{5}-10=1+6\sqrt{5}\)