Question

Rút gọn các biểu thức :

\(a,\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)

\(b,\frac{\sqrt{3}+\sqrt{11+6\sqrt{2}}-\sqrt{5+2\sqrt{6}}}{\sqrt{2}+\sqrt{6+2\sqrt{5}}-\sqrt{7+2\sqrt{10}}}\)

Answer 1

a/

\(=\sqrt{6-2\sqrt{5}}\left(\sqrt{5}-1\right)\frac{\left(6+2\sqrt{5}\right)}{2}=\sqrt{\left(\sqrt{5}-1\right)^2}\left(\sqrt{5}-1\right)\frac{\left(\sqrt{5}+1\right)^2}{2}\)

\(=\left(\sqrt{5}-1\right)^2.\frac{\left(\sqrt{5}+1\right)^2}{2}=\frac{\left(5-1\right)^2}{2}=8\)

b/

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