\(=\sqrt{6+2\sqrt{2}\cdot\sqrt{3-\sqrt{\sqrt{2}+2\sqrt{3}+4-\sqrt{2}}}}\)
\(=\sqrt{6+2\sqrt{2}\cdot\sqrt{3-\sqrt{3}-1}}\)
\(=\sqrt{6+2\cdot\sqrt{4-2\sqrt{3}}}\)
\(=\sqrt{6+2\sqrt{3}-2}=\sqrt{4+2\sqrt{3}}=\sqrt{3}+1\)
rút gọn biểu thức
A=\(\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{2+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
D = ( \(\sqrt{3}-1\)) . \(\sqrt{6+2\sqrt{2}.\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}\)
Rút gọn
B=\(\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
Rút gọn biểu thức
\(A=\sqrt{30+12\sqrt{6}}-\sqrt{21-6\sqrt{6}}\)
\(B=\sqrt{2+\sqrt{2}}.\sqrt{2+\sqrt{2+2}}.\sqrt{2-\sqrt{2+2}}\)
1:Tính A=\(\sqrt{4+\sqrt{7}}\)-\(\sqrt{4-\sqrt{7}}+\left(\sqrt{3}+1\right)\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
Rút gọn các biểu thức sau:
a) \(\dfrac{2}{5}\sqrt{75}-0,5\sqrt{48}+\sqrt{300}-\dfrac{2}{3}\sqrt{12}\)
b) \(\dfrac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}+\dfrac{3}{3+\sqrt{6}}\)
c) \(3\sqrt{2}-2\sqrt{3}+2\sqrt{3}+3\sqrt{2}\)
d) \(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
e) \(\dfrac{\sqrt{a}-\sqrt{b}^2+4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\dfrac{a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}}\) với a > 0, b > 0
Rút gọn:
D= \(\left(\sqrt{3}-1\right)\) . \(\sqrt{6+2\sqrt{2}.\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18}-\sqrt{128}}}\)
Mọi người giúp em vs ak, em đang cần gấp lắm
Câu 1: Rút gọn:
a) \(2\sqrt{18}-4\sqrt{50}-3\sqrt{32}\)
b) \(\sqrt{14-6\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)
c) \(\dfrac{\sqrt{10}+10}{1+\sqrt{10}}-\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}\)
Câu 2: Giải phương trình:
\(\sqrt{9x^2-30x+25}=5\)
* 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.\(\left(\dfrac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\dfrac{5}{\sqrt{5}}\right):\left(\dfrac{1}{\sqrt{5}-\sqrt{2}}\right)\)
