Question

Giúp mình tính bài này với ạ =)) cần gấp.

a) \(\left(2+\sqrt{4+\sqrt{6-2\sqrt{5}}}\right)\cdot\left(\sqrt{10}-\sqrt{2}\right)\)

b) \(\sqrt{6-2\sqrt{2}+\sqrt{12}+\sqrt{18-8\sqrt{2}}}\)

c) \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)

d) \(\sqrt{13+6\sqrt{4+\sqrt{9-4\sqrt{2}}}}-3\sqrt{2}\)

Answer 1

c/ = \(\sqrt{13+30\sqrt{2+\sqrt{8+2.2\sqrt{2}+1}}}\)

\(=\sqrt{13+30\sqrt{3+2\sqrt{2}}}\)

\(=\sqrt{43+30\sqrt{2}}\)

\(=\sqrt{25+2.3.5.\sqrt{2}+18}\)

\(=5+3\sqrt{2}\)

Answer 2

d/ \(=\sqrt{13+6\sqrt{4+\sqrt{9-4\sqrt{2}}}}\)

\(=\sqrt{13+6\sqrt{4+2\sqrt{2}-1}}\)

\(=\sqrt{13+6\left(\sqrt{3}+1\right)}\)

\(=\sqrt{19+6\sqrt{2}}\)

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