Đặt \(A=\sqrt{4-\sqrt{15}}-\sqrt{4+\sqrt{15}}+\sqrt{6}\)
\(\Rightarrow\sqrt{2}.A=\sqrt{8-2\sqrt{15}}+\sqrt{8+2\sqrt{15}}+2\sqrt{3}\)
\(\Rightarrow\sqrt{2}.A=\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}+2\sqrt{3}\)
\(\Rightarrow\sqrt{2}.A=\sqrt{5}-\sqrt{3}-\sqrt{5}-\sqrt{3}+2\sqrt{3}\)
\(\Rightarrow\sqrt{2}.A=0\Rightarrow A=0\)
Chứng minh rằng: (4+\(\sqrt{15}\))(\(\sqrt{10}-\sqrt{6}\))\(\sqrt{4-\sqrt{15}}\)=2
\(\left(4+\sqrt{15}\right)\left(\sqrt{10}+\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
Dạng 3.Chứng minh đẳng thức
Bài 1: CM
a)\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}=2\)
b)\(\left(5+\sqrt{21}\right)\left(\sqrt{14}-\sqrt{6}\right)\sqrt{5-\sqrt{21}}=8\)
Bài 2 :CM
\(\dfrac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{2}}=\sqrt{\sqrt{5}+1}\)
Rút gọn
A=\(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
B=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+\sqrt{2\sqrt{5}}}}\)
Rút gọn:
\(2\left(\sqrt{10}-\sqrt{2}\right)\sqrt{4+\sqrt{6-2\sqrt{5}}}\)
\(\left(4\sqrt{2}+\sqrt{30}\right)\left(\sqrt{5}-\sqrt{3}\right)\sqrt{4-\sqrt{15}}\)
Thực hiện phép tính : \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right).\sqrt{4-\sqrt{15}}\)
Thực hiện phép tính
a) \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b) \(\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}}\left(3+\sqrt{5}\right)\)
c) \(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{2}\)
d) \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{7}\)
e) \(\sqrt{6,5+\sqrt{12}}+\sqrt{6,5-\sqrt{12}}+2\sqrt{6}\)
Rút gọn các biểu thức :
a) \(\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{4-2\sqrt{3}}\)
b) \(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
c) \(\left(15\sqrt{200}-3\sqrt{450}+2\sqrt{50}\right):\sqrt{10}\)
rút gọn biểu thức sau: \(\sqrt{4+\sqrt{15}}-\sqrt{4-\sqrt{15}}\)
