Question

rút gọn các biểu thức sau

a) \(\sqrt{5+2\sqrt{ }6}+\sqrt{14-4\sqrt{ }6}\)

b) \(\sqrt{5-2\sqrt{ }6}+\sqrt{11-4\sqrt{ }6}\)

c) phân tích 11-\(\sqrt{33}\) thành nhân tử

Answer 1

a/ \(\sqrt{5+2\sqrt{6}}+\sqrt{14-4\sqrt{6}}=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}+\sqrt{\left(2\sqrt{3}-\sqrt{2}\right)^2}=\left|\sqrt{3}+\sqrt{2}\right|+\left|2\sqrt{3}-\sqrt{2}\right|=\sqrt{3}+\sqrt{2}+2\sqrt{3}-\sqrt{2}=3\sqrt{3}\) (Vì \(\sqrt{3}+\sqrt{2}>0\) , \(2\sqrt{3}-\sqrt{2}>0\) )

b/ \(\sqrt{5-2\sqrt{6}}+\sqrt{14-4\sqrt{6}}=\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}+\sqrt{\left(2\sqrt{3}-\sqrt{2}\right)^2}=\left|\sqrt{3}-\sqrt{2}\right|+\left|2\sqrt{3}-\sqrt{2}\right|=\sqrt{3}-\sqrt{2}+2\sqrt{3}-\sqrt{2}=3\sqrt{3}-2\sqrt{2}\)

c/ \(11-\sqrt{33}=\sqrt{11}.\sqrt{11}-\sqrt{3}.\sqrt{11}=\sqrt{11}\left(\sqrt{11}-\sqrt{3}\right)\)