\(A=\sqrt{4+\sqrt{7}}-\sqrt{4+\sqrt{7}}\Leftrightarrow\sqrt{2}A=\sqrt{8+2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)
\(\Leftrightarrow\sqrt{2}A=\sqrt{\sqrt{7}^2+2\sqrt{7}+1}-\sqrt{\sqrt{7}^2+2\sqrt{7}+1}\)
\(\Leftrightarrow\sqrt{2}A=\sqrt{7}+1-\sqrt{7}-1=0\)
\(\Leftrightarrow A=0\)
a) \(\sqrt{8+2\sqrt{15}}-\sqrt{6+2\sqrt{5}}\)
b) \(\sqrt{17-2\sqrt{72}}+\sqrt{19+2\sqrt{18}}\)
c) \(\sqrt{12-2\sqrt{32}}+\sqrt{9+4\sqrt{2}}\)
đề bài là rút gọn biểu thức
giải chi tiết hộ mình ạ !!!
Rút gọn biểu thức
a) \(\left(3-\sqrt{15}\right)\sqrt{4+\sqrt{15}}\)
b) \(\sqrt{29-12\sqrt{5}}-\sqrt{24-8\sqrt{5}}\)
Rút gọn: \(M=\dfrac{8}{\sqrt{5}-\sqrt{3}}+\dfrac{7}{\sqrt{3}-2}+\dfrac{4}{\sqrt{2}-1}+\dfrac{3\sqrt{5}-\sqrt{15}}{\sqrt{15}}\)
rút gọn biểu thức :
A= \(\dfrac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}+\sqrt{27-10\sqrt{2}}\).
B= \(\dfrac{\sqrt{2-\sqrt{3}}+\sqrt{4-\sqrt{15}}+\sqrt{10}}{\sqrt{23-3\sqrt{5}}}\).
C= \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\).
rút gọn biểu thức: a)\(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)
b)\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
c)\(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
Rút gọn
A=\(\sqrt{8-2\sqrt{15}}\)
B=\(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)
C=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
D=\(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
Rút gọn biểu thức:\(A=\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}\)
Rút gọn các biểu thức sau:
a. \(\dfrac{8}{\left(\sqrt{5}+\sqrt{3}\right)^2}\) - \(\dfrac{8}{\left(\sqrt{5}-\sqrt{3}\right)^2}\)
b.\(\dfrac{1}{4-3\sqrt{2}}\) - \(\dfrac{1}{4+3\sqrt{2}}\)
c.\(\left(\dfrac{\sqrt{7}+3}{\sqrt{7}-3}-\dfrac{\sqrt{7}-3}{\sqrt{7}+3}\right)\): \(\sqrt{28}\)
d.\(\dfrac{3}{\sqrt{6}-\sqrt{3}}\)+\(\dfrac{4}{\sqrt{7}+\sqrt{3}}\)
Rút gọn các biểu thức sau :
a/\(\sqrt{4-\sqrt{15}} -\sqrt{2+\sqrt{3}}\)
b/\(\sqrt{4+\sqrt{15}}+ \sqrt{7-\sqrt{45}}\)
c/\(\sqrt{6+2\sqrt{5-\sqrt{13+4\sqrt{3}}}} -\sqrt{6-2\sqrt{5+\sqrt{13-4\sqrt{3}}}}\)
