\(\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}=\sqrt{5-2\sqrt{5}.\sqrt{3}+3}-\sqrt{5+2.\sqrt{5}.\sqrt{3}+3}=\sqrt{5}-\sqrt{3}-\sqrt{5}-\sqrt{3}=-2\sqrt{3}\)
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
\(\dfrac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{2}}=\sqrt{\sqrt{5}+1}\)
thực hiện phép tính:
a)\(\dfrac{1}{1+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+...+\dfrac{1}{\sqrt{2018}+\sqrt{2019}}\)
b)\(\sqrt{8-2\sqrt{15}}+\sqrt{4-2\sqrt{3}}\)
1,Rút gọn
a, \(\left(2\sqrt{2}-1\right)\left(\sqrt{8}+1\right)\)
b, \(\left(\sqrt{12}+\sqrt{75}-2\sqrt{27}\right):\sqrt{3}\)
c, \(\sqrt{3+2\sqrt{2}}+\sqrt{6-4\sqrt{2}}\)
d, \(\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)
e, \(\left(\sqrt{3}-\sqrt{2}\right)\sqrt{5+2\sqrt{6}}\)
f, \(\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{15}}\)
A=\(\sqrt{5-2\sqrt{6}}\)
B=\(\sqrt{7+2\sqrt{10}}+\sqrt{7-2\sqrt{10}}\)
C= \(\sqrt{8+2\sqrt{15}}-\sqrt{5}\)
\(\sqrt{8-\sqrt{15}}-\sqrt{8+\sqrt{15}}\).Hãy rút gọn biểu thức
Thực hiện phép tính:
a) \(\sqrt{8+\sqrt{60}}-\sqrt{\dfrac{2}{\sqrt{15}+4}}\)
Mình đang cần gấp ạ
Chứng minh rằng: (4+\(\sqrt{15}\))(\(\sqrt{10}-\sqrt{6}\))\(\sqrt{4-\sqrt{15}}\)=2
rút gọn biểu thức
\(B=21\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}\right)^2-6\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}\right)^2-15\sqrt{15}\)
\(\dfrac{2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3}{2\sqrt{5}-2\sqrt{10}-\sqrt{3}-\sqrt{6}}\)
