Question

rút gọn

L= \(\left(\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}\right).\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)\)

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Answer 1

Lời giải:

\(L=(\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16})(\sqrt{2}+\sqrt{3}+\sqrt{4})\)

\(=(\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4)(\sqrt{2}+\sqrt{3}+\sqrt{4})\)

\(=(\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{4}+\sqrt{6}+\sqrt{8})(\sqrt{2}+\sqrt{3}+\sqrt{4})\)

\(=[(\sqrt{2}+\sqrt{3}+\sqrt{4})+\sqrt{2}(\sqrt{2}+\sqrt{3}+\sqrt{4})](\sqrt{2}+\sqrt{3}+\sqrt{4})\)

\(=(1+\sqrt{2})(\sqrt{2}+\sqrt{3}+\sqrt{4})^2\)

\(=(1+\sqrt{2})(\sqrt{2}+\sqrt{3}+2)^2\)