Question

rút gọn biểu thức sau

a/\(\sqrt{6+2\sqrt{5}}\) - \(\sqrt{6-2\sqrt{5}}\)

b/ \(\sqrt{7+3\sqrt{6}}\)+ \(\sqrt{7-2\sqrt{6}}\)- \(2\sqrt{6}\)

c/ \(\sqrt{9+4\sqrt{5}}\) +\(\sqrt{9-4\sqrt{5}}\)- \(2\sqrt{5}\)

Answer 1

a)

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

b) Sửa đề:

\(\sqrt{7+2\sqrt{6}}+\sqrt{7-2\sqrt{6}}-2\sqrt{6}\\ =\sqrt{\left(\sqrt{6}+1\right)^2}+\sqrt{\left(\sqrt{6}-1\right)^2}-2\sqrt{6}\\ =\sqrt{6}+1+\sqrt{6}-1-2\sqrt{6}\\ =0\)

c)

\(\sqrt{9+4\sqrt{5}}+\sqrt{9-4\sqrt{5}}-2\sqrt{5}\\ =\sqrt{9+2\sqrt{20}}+\sqrt{9-2\sqrt{20}}-2\sqrt{5}\\ =\sqrt{\left(\sqrt{5}+2\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}-2\sqrt{5}\\ =\sqrt{5}+2+\sqrt{5}-2-2\sqrt{5}\\ =0\)