\(VT=\left(\dfrac{\sqrt{6}\left(\sqrt{2}-1\right)}{2\left(\sqrt{2}-1\right)}-\dfrac{6\sqrt{6}}{3}\right)\cdot\dfrac{1}{\sqrt{6}}\)
\(=\left(\dfrac{\sqrt{6}}{2}-2\sqrt{6}\right)\cdot\dfrac{1}{\sqrt{6}}\)
\(=\dfrac{1}{2}-2=-\dfrac{3}{2}\)
\(\left(\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\dfrac{\sqrt{216}}{3}\right).\dfrac{1}{\sqrt{6}}\)
Chứng minh đẳng thức:
a) \(\dfrac{\sqrt{a}+\sqrt{b}}{2\sqrt{a}-2\sqrt{b}}-\dfrac{\sqrt{a}-\sqrt{b}}{2\sqrt{a}-2\sqrt{b}}-\dfrac{2b}{\sqrt{a}-\sqrt{b}}\)
b) \(\left(\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\dfrac{\sqrt{216}}{3}\right).\dfrac{1}{\sqrt{6}}=\dfrac{-3}{2}\)
* Rút gọn các biểu thức
a. \(\sqrt{\left(3-\sqrt{2}\right)^2}+\sqrt{2\left(-5\right)^2}\)
b. \(\dfrac{\sqrt[3]{625}}{\sqrt[3]{5}}-\sqrt[3]{-4}.\sqrt[3]{2}\)
c. \(6\sqrt{\dfrac{1}{2}}-\dfrac{2}{\sqrt{2}}-3\sqrt{8}\)
d. \(\dfrac{\sqrt{6}-\sqrt{3}}{\sqrt{2}-1}-\dfrac{2}{\sqrt{3}-1}\)
Rút gọn
\(\left(\sqrt{\dfrac{2}{3}}+\sqrt{\dfrac{3}{2}+2}\right)\left(\dfrac{\sqrt{2}+\sqrt{3}}{4\sqrt{2}}-\dfrac{\sqrt{3}}{2+\sqrt{3}}\right)\left(24+8\sqrt{6}\right)\left(\dfrac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}+\dfrac{\sqrt{3}}{\sqrt{2}-\sqrt{3}}\right)\)
* Rút gọn biểu thức
a. \(\left(2\sqrt{125}-3\sqrt{5}-\sqrt{180}\right):\left(-\sqrt{5}\right)+\sqrt{8}\)
b. \(\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}+\sqrt{18}\)
c. \(\sqrt{48}-6\sqrt{\dfrac{1}{3}}+\dfrac{\sqrt{3}-3}{\sqrt{3}}\)
d.\(\left(\dfrac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\dfrac{5}{\sqrt{5}}\right):\left(\dfrac{1}{\sqrt{5}-\sqrt{2}}\right)\)
\(A=\dfrac{1}{\sqrt{8}+\sqrt{7}}+\sqrt{175}+2\sqrt{2}\\ B=\left(5+2\sqrt{6}\right)\cdot\left(49-20\sqrt{6}\right)\cdot\sqrt{5-2\sqrt{6}}\)
\(C=\dfrac{1}{2}\left(\sqrt{6}+\sqrt{5}\right)^2-\dfrac{1}{4}\sqrt{120}-\sqrt{\dfrac{15}{2}}\)
\(D=\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}+\dfrac{1}{4}\sqrt{8}\right)\cdot3\sqrt{6}\)
* Chứng minh đẳng thức
\(\left(\dfrac{\sqrt{30}-\sqrt{20}}{\sqrt{3}-\sqrt{2}}-\dfrac{6}{\sqrt{6}}\right)\sqrt{4+\sqrt{15}}=2\)
rg: \(\sqrt{\left(\sqrt{7}-4\right)}^2\) = 3
chứng minh:
\(\left(\sqrt{8}-5\sqrt{2}+\sqrt{20}\right)\sqrt{5}-\left(3\sqrt{\dfrac{1}{10}}+10\right)=3.3\sqrt{10}\)
\(\left(\sqrt{12}-6\sqrt{3}+\sqrt{24}\right)\sqrt{6}\left(5\sqrt{\dfrac{1}{2}}+12\right)=-14.5\sqrt{2}\)
Thực hiện phép tính
-\(\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}\)
- \(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
-\(\dfrac{\left(5+\sqrt{2}\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)
- \(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
- \(\dfrac{\sqrt{3}}{1-\sqrt{\sqrt{3}+1}}+\dfrac{\sqrt{3}}{1+\sqrt{\sqrt{3}+1}}\)
