Question

[Đoàn Thị Thùy]

 Rút gọn các biểu thức sau:

a)\(\sqrt{\sqrt{5}-\sqrt{9-\sqrt{29+12\sqrt{5}}}}\)

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

Answer 1

[Hacker♪]

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

\(=\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}\right)^2}+4\sqrt{2}+1^2}}\)

\(=\sqrt{13+30\sqrt{2+2\sqrt{2}+1^2}}\)

\(=\sqrt{13+30\sqrt{\left(\sqrt{2}\right)^2+2\sqrt{2}+1^2}}\)

\(=\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\)

\(=\sqrt{5^2+2.5.3\sqrt{2}+\left(3+\sqrt{2}\right)^2}\)

\(=\sqrt{\left(5+3+\sqrt{2}\right)^2}\)

\(=\sqrt{\left(5+6\right)}=\sqrt{11}\)

\(=5+6=11\)

Answer 2

[Nguyễn Thùy Dương]

a)=1
b)=\(3\sqrt{2}+5\)