Question

[Nguyễn Thị Hải Yến]

Phân tích :

1) \(\sqrt{29+12\sqrt{5}}\)  -  \(\sqrt{29-12\sqrt{5}}\)

2) \(\sqrt{8-2\sqrt{15}}\)-  \(\sqrt{23-4\sqrt{15}}\)

3) \(\sqrt{8-2\sqrt{15}}\) + \(\sqrt{48+6\sqrt{15}}\)

4) \(\sqrt{49-5\sqrt{96}}\)+\(\sqrt{49+5\sqrt{96}}\)

5)  \(\sqrt{15-6\sqrt{15}}\)+\(\sqrt{33-12\sqrt{6}}\)

6) \(\sqrt{16-6\sqrt{7}}\)+\(\sqrt{64-24\sqrt{7}}\)

7) \(\sqrt{14-6\sqrt{5}}\)+\(\sqrt{14+6\sqrt{5}}\)

8) \(\sqrt{1-6\sqrt{2}}\)+\(\sqrt{11-6\sqrt{2}}\)

9) \(\sqrt{13+4\sqrt{10}}\)+\(\sqrt{13-4\sqrt{10}}\)

10) \(\sqrt{46-6\sqrt{5}}\)+\(\sqrt{29-12\sqrt{5}}\)

Answer 1

[Bui Huyen]

\(\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}=\left(2\sqrt{5}+3\right)-\left(2\sqrt{5}-3\right)=6\)

\(\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{15}}=\left(\sqrt{5}-\sqrt{3}\right)-\left(2\sqrt{5}-\sqrt{3}\right)=-\sqrt{5}\)

\(\sqrt{8-12\sqrt{5}}+\sqrt{48+6\sqrt{15}}=\left(\sqrt{5}-\sqrt{3}\right)+\left(3\sqrt{5}+\sqrt{3}\right)=4\sqrt{5}\)

\(\sqrt{49-5\sqrt{96}}+\sqrt{49+5\sqrt{96}}=\left(5-2\sqrt{6}\right)+\left(5+2\sqrt{6}\right)=10\)

\(\sqrt{15-6\sqrt{15}}+\sqrt{33-12\sqrt{6}}\) đề này sai ạ

\(\sqrt{16-6\sqrt{7}}+\sqrt{64-24\sqrt{7}}=\left(3-\sqrt{7}\right)+\left(6-2\sqrt{7}\right)=9-3\sqrt{7}\)

\(\sqrt{14-6\sqrt{5}}+\sqrt{14+6\sqrt{5}}=\left(3-\sqrt{5}\right)+\left(3+\sqrt{5}\right)=6\)

\(\sqrt{1-6\sqrt{2}}+\sqrt{11-6\sqrt{2}}\)

\(\sqrt{13+4\sqrt{10}}+\sqrt{13-4\sqrt{10}}=\left(2\sqrt{2}+5\right)+\left(2\sqrt{2}-5\right)=4\sqrt{2}\)

\(\sqrt{46-6\sqrt{5}}+\sqrt{29-12\sqrt{5}}=\left(3\sqrt{5}-1\right)+\left(2\sqrt{5}-3\right)=5\sqrt{5}-4\)

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