\(\sqrt{10+\sqrt{60}-\sqrt{24}-\sqrt{40}}\)

\(=\sqrt{2+3+5+2\sqrt{6}+2\sqrt{10}+2\sqrt{15}}\)

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

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

\(\sqrt{10+2\sqrt{15}+2\sqrt{6}+2\sqrt{10}}\)

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

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

giải ra chưa chỉ mình với

Bạn áp dụng hằng đẳng thức (a+b+c)^2= a^2+b^2+c^2+2(ab+ac+bc)

\(\sqrt{10+\sqrt{24}+\sqrt{40}+\sqrt{60}}=\sqrt{2+3+5+2\sqrt{2.3}+2\sqrt{2.5}+2\sqrt{3.5}}\)

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

Muội chả hỉu sao tỷ học giỏi vậy!

a/ \(\sqrt{2}+\sqrt{6}\)

b/ Sửa đề:

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

c/ \(1+\sqrt{2}+\sqrt{5}\)

giải rõ ra hộ mình với

a/ \(2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}\)

\(=2\sqrt{3+\sqrt{5-\sqrt{12+2.2\sqrt{3}+1}}}\)

\(=2\sqrt{3+\sqrt{5-\sqrt{\left(2\sqrt{3}+1\right)^2}}}\)

\(=2\sqrt{3+\sqrt{5-\left(2\sqrt{3}+1\right)}}\)

\(=2\sqrt{3+\sqrt{4-2\sqrt{3}}}\)

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

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

\(=2\sqrt{3+\left(\sqrt{3}-1\right)}\)

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

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

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

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

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