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\(\sqrt{8+2\sqrt{2}+2\sqrt{5}+2\sqrt{10}}-\sqrt{7+2\sqrt{10}}\)
\(=\sqrt{\sqrt{2}^2+\sqrt{5}^2+1^2+2\sqrt{2}+2\sqrt{5}+2\sqrt{2}.\sqrt{5}}-\sqrt{\sqrt{5}^2+2\sqrt{10}+\sqrt{2}^2}\)
\(=\sqrt{\left(\sqrt{5}+\sqrt{2}+1\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\)
\(=\sqrt{5}+\sqrt{2}+1-\sqrt{5}-\sqrt{2}\)
\(=1\)
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\(\sqrt{8+2\sqrt{2}+2\sqrt{5}+2\sqrt{10}}\)=\(\sqrt{2+5+1+2\sqrt{2}+2\sqrt{5}+2\sqrt{2}\cdot\sqrt{5}}\)
=\(\sqrt{\left(\sqrt{2}+\sqrt{5}+1\right)^2}=\sqrt{2}+\sqrt{5}+1\)
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\(\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
\(=\sqrt{1+2+5+2\left(\sqrt{2}+\sqrt{5}+\sqrt{10}\right)}=\sqrt{\left(1+\sqrt{2}+\sqrt{5}\right)^2}\)
\(=1+\sqrt{2}+\sqrt{5}\)
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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/ \(1+\sqrt{2}+\sqrt{5}\)