Question

bài 1 : rút gọn

a)\(\sqrt{7-2\sqrt{10}}+\sqrt{7+2\sqrt{10}}\)

b)\(\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}\)

c)\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)

bài 2

a)\(\frac{\sqrt{7}-\sqrt{14}}{1-\sqrt{2}}\)

b)\(\frac{\sqrt{6}-5\sqrt{3}}{2\sqrt{2}-10}\)

c) \(\frac{7-2\sqrt{10}}{5-\sqrt{10}}\)

Answer 1

1.

a, \(\sqrt{7-2\sqrt{10}}+\sqrt{7+2\sqrt{10}}=\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\)

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

b, \(\sqrt{8-2\sqrt{15}}+\sqrt{8-2\sqrt{15}}=\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}\)

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

c, \(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}=\frac{\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}}{\sqrt{2}}\)

\(=\frac{\sqrt{\left(\sqrt{5}-1\right)^2}+\sqrt{\left(\sqrt{5}+1\right)^2}}{\sqrt{2}}=\frac{\sqrt{5}-1+\sqrt{5}+1}{\sqrt{2}}=\frac{2\sqrt{5}}{\sqrt{2}}=\sqrt{10}\)