Ta có: \(\sqrt{3+\sqrt{5}}+\sqrt{7-3\sqrt{5}}-\sqrt{2}\)
\(=\frac{\sqrt{6+2\sqrt{5}}+\sqrt{14-6\sqrt{5}}-2}{\sqrt{2}}\)
\(=\frac{\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(3-\sqrt{5}\right)^2}-2}{\sqrt{2}}\)
\(=\frac{\sqrt{5}+1+3-\sqrt{5}-2}{\sqrt{2}}\)(vì \(\left\{{}\begin{matrix}\sqrt{5}>1>0\\3>\sqrt{5}\end{matrix}\right.\))
\(=\frac{2}{\sqrt{2}}=\sqrt{2}\)
\(\sqrt{3-2\sqrt{2}}-\sqrt{11+6\sqrt{2}}\)
\(\sqrt{4-2\sqrt{3}}-\sqrt{7-4\sqrt{3}}+\sqrt{19+8\sqrt{3}}\)
\(\sqrt{6-2\sqrt{5}}+\sqrt{9+4\sqrt{5}}-\sqrt{14-6\sqrt{5}}\)
\(\sqrt{11-4\sqrt{7}}+\sqrt{23-8\sqrt{7}}+\sqrt{\left(-2^6\right)}\)
rút gọn:giải chi tiết hộ mình nha
Tính ;
a) \(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}.}\sqrt{2-\sqrt{2+\sqrt{2}}}\)
b) \(\sqrt{47+\sqrt{5}}.\sqrt{7-\sqrt{2+\sqrt{5}}}.\sqrt{7+\sqrt{2+\sqrt{5}}}\)
c) \(\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
d) \(\sqrt{31+\sqrt{2}}.\sqrt{6+\sqrt{5+\sqrt{2}}}\sqrt{3+\sqrt{3+\sqrt{5+\sqrt{2}}}}.\sqrt{3-\sqrt{3+\sqrt{5+\sqrt{2}}}}\)
Tính
\(A=\sqrt{20}-3\sqrt{8}+5\sqrt{45}\)
\(B=\dfrac{30}{\sqrt{7}-1}+\dfrac{15}{\sqrt{7}+2}\)
\(C=\left(3-\dfrac{5-\sqrt{5}}{\sqrt{5}-1}\right)\left(3+\dfrac{5+\sqrt{5}}{\sqrt{5}+1}\right)\)
\(D=\sqrt{\left(3-\sqrt{2}\right)^2}-\sqrt{\left(1-\sqrt{2}\right)^2}\)
\(E=\sqrt{7-4\sqrt{3}}-\sqrt{3+2\sqrt{3}}\)
* Trục căn thức ở mẫu
a. \(\dfrac{7}{\sqrt{5}-\sqrt{3}-\sqrt{7}}\)
b. \(\dfrac{5}{2-\sqrt{3}-\sqrt{5}}\)
c. \(\dfrac{59}{\sqrt[3]{5}+\sqrt{3}-\sqrt{2}}\)
* Trục căn thức ở mẫu
a. \(\dfrac{7}{\sqrt{5}-\sqrt{3}-\sqrt{7}}\)
b. \(\dfrac{5}{2-\sqrt{3}-\sqrt{5}}\)
c. \(\dfrac{59}{\sqrt[3]{5}+\sqrt{3}-\sqrt{2}}\)
* Thực hiện phép tính.
a.\(2\sqrt{18}-9\sqrt{50}+3\sqrt{8}\)
b.\(\left(\sqrt{7}-\sqrt{3}\right)^2+7\sqrt{84}\)
c.\(\left(\dfrac{6-2\sqrt{2}}{3-\sqrt{2}}-\dfrac{5}{\sqrt{5}}\right).\dfrac{1}{2-\sqrt{5}}\)
d.\(\sqrt{\left(2-\sqrt{5}\right)^2-\sqrt{5}}\)
rút gọn :
a)\(\left(\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}+\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
b) \(\sqrt{\dfrac{3\sqrt{3}-4}{2\sqrt{3}+1}}+\sqrt{\dfrac{\sqrt{3}+4}{5-2\sqrt{3}}}\)
c) \(\dfrac{2\sqrt{5}-5\sqrt{2}}{\sqrt{2}-\sqrt{5}}+\dfrac{6}{2-\sqrt{10}}+\sqrt{67+12\sqrt{7}}\)
d) \(\left(\dfrac{\sqrt{5}}{\sqrt{2}+1}+\dfrac{14}{2\sqrt{2}-1}-\dfrac{6}{2-\sqrt{2}}\right).\sqrt{17-12\sqrt{2}}\)
Không dùng máy tính hãy so sánh:
\(A=\dfrac{3+\sqrt{5}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}+\dfrac{3-\sqrt{5}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
\(B=\dfrac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4+\sqrt{7}}}+\dfrac{4-\sqrt{7}}{3\sqrt{2}-\sqrt{4-\sqrt{7}}}\)
* Trục căn thức ở mẫu
a. \(\dfrac{7}{\sqrt{5}-\sqrt{3}+\sqrt{7}}\)
b. \(\dfrac{5}{1-\sqrt{2}-\sqrt{3}}\)
c. \(\dfrac{59}{\sqrt[3]{5}+\sqrt{3}+\sqrt{2}}\)
* Trục căn thức ở mẫu
a. \(\dfrac{7}{\sqrt{5}-\sqrt{3}+\sqrt{7}}\)
b. \(\dfrac{5}{1-\sqrt{2}-\sqrt{3}}\)
c.\(\dfrac{59}{\sqrt[3]{5}+\sqrt{3}+\sqrt{2}}\)
