\(\left(\sqrt{10}+\sqrt{2}\right)\left(6-2\sqrt{5}\right)\sqrt{3+\sqrt{5}}=\left(\sqrt{5}+1\right)\left(6-2\sqrt{5}\right)\sqrt{6+2\sqrt{5}}\)
\(=\left(\sqrt{5}+1\right)\left(6-2\sqrt{5}\right)\sqrt{\left(\sqrt{5}+1\right)^2}=\left(\sqrt{5}+1\right)\left(6-2\sqrt{5}\right)\left(\sqrt{5}+1\right)\)
\(=\left(\sqrt{5}+1\right)^2\left(6-2\sqrt{5}\right)=\left(6+2\sqrt{5}\right)\left(6-2\sqrt{5}\right)\)
\(=36-4.5=16\)
\(\sqrt{2}-\sqrt{3}\left(\sqrt{6}-\sqrt{2}\right)\left(2+\sqrt{3}\right)\) em xem lại đề câu này, vẫn rút gọn được nhưng biểu thức nó hơi kì quặc
\(\left(\sqrt{11+2\sqrt{30}}-\sqrt{8-4\sqrt{3}}\right)\left(\sqrt{5}-\sqrt{2}\right)=\left(\sqrt{\left(\sqrt{6}+\sqrt{5}\right)^2}-\sqrt{\left(\sqrt{6}-\sqrt{2}\right)^2}\right)\left(\sqrt{5}-\sqrt{2}\right)\)
\(=\left(\sqrt{6}+\sqrt{5}-\left(\sqrt{6}-\sqrt{2}\right)\right)\left(\sqrt{5}-\sqrt{2}\right)=\left(\sqrt{5}+\sqrt{2}\right)\left(\sqrt{5}-\sqrt{2}\right)\)
\(=5-2=3\)
\(\sqrt{2-\sqrt{3}}\left(\sqrt{6}-\sqrt{2}\right)\left(2+\sqrt{3}\right)=\sqrt{4-2\sqrt{3}}\left(\sqrt{3}-1\right)\left(2+\sqrt{3}\right)\)
\(=\sqrt{\left(\sqrt{3}-1\right)^2}\left(\sqrt{3}-1\right)\left(2+\sqrt{3}\right)=\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)\left(2+\sqrt{3}\right)\)
\(=\left(\sqrt{3}-1\right)^2\left(2+\sqrt{3}\right)=\left(4-2\sqrt{3}\right)\left(2+\sqrt{3}\right)=2\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)\)
\(=2\left(4-3\right)=2\)
