\(\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-8\sqrt{2}}}}\)
= \(\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12+\sqrt{\left(4-\sqrt{2}\right)^2}}}}\)
= \(\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+4-\sqrt{2}}}\)
= \(\sqrt{6-2\sqrt{4+2\sqrt{3}}}\)
= \(\sqrt{6-2\sqrt{\left(\sqrt{3}+1\right)^2}}\)
= \(\sqrt{4-2\sqrt{3}}\)
= \(\sqrt{\left(\sqrt{3}-1\right)^2}\)
= \(\sqrt{3}-1\)
Rút gọn các biểu thức sau :
a,\(\dfrac{\sqrt{6}+\sqrt{10}}{\sqrt{21}+\sqrt{35}}\)
b,\(\dfrac{\sqrt{405}+3\sqrt{27}}{3\sqrt{3}+\sqrt{45}}\)
c,\(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}-\sqrt{6}-\sqrt{9}-\sqrt{12}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
d, D=\(\dfrac{2}{x^2-y^2}\cdot\sqrt{\dfrac{9\left(x^2+2xy+y^2\right)}{4}}\) \(\left(vớix\ne y,x\ne-y\right)\)
Rút gọn :
a) \(\dfrac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\)
b) \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
Rút gọn biểu thức:
a) \(\sqrt{6+2\sqrt{4-2\sqrt{3}}}\)
b) \(\sqrt{6-2\sqrt{3+\sqrt{13+4\sqrt{3}}}}\)
c) \(\sqrt{\sqrt{3}+\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
d) \(\sqrt{23-6\sqrt{10+4\sqrt{3-2\sqrt{2}}}}\)
B3: Rút gọn :
a, \(\sqrt{3}+\sqrt{8-2\sqrt{5}}\)
b, \(\sqrt{x-1-2\sqrt{x-2}}\)
rút gọn biểu thức
A=\(\sqrt{27}\)-2\(\sqrt{12}\)-\(\sqrt{75}\)
Rút gọn :
a) \(\dfrac{3\sqrt{2-6}}{\sqrt{2-1}}\)
b) \(\dfrac{3\sqrt{5}+5\sqrt{3}}{\sqrt{3}+\sqrt{5}}\)
c) \(\dfrac{x-y}{\sqrt{x}-\sqrt{y}}\)
rút gọn biểu thức
a) \(3\sqrt{8}-4\sqrt{18}+5\sqrt{32}-\sqrt{50}\)
b) (\(15\sqrt{50}+5\sqrt{200}-3\sqrt{450}\)) : 10
c) \(2\sqrt{28}+2\sqrt{63}-3\sqrt{175}+\sqrt{112}\)
d) (\(\sqrt{14}-3\sqrt{2}\))\(^2\) +\(6\sqrt{28}\)
e) \(\sqrt{\left(1-\sqrt{2018}\right)^2}\). \(\sqrt{2019+2\sqrt{2018}}\)
f) \(\left(\sqrt{6}-\sqrt{5}\right)^2-\sqrt{120}\)
g)\(12\left(2\sqrt{3}-3\sqrt{2}\right)^2+2\sqrt{6}+3\sqrt{4}\)
Rút gọn : \(A=\sqrt{\sqrt{2}-1}+\sqrt{\sqrt{2}+1}-\sqrt{2\sqrt{2}+2}\)
Tính
1) \(\sqrt{18}.\sqrt{2}\)
2) \(\sqrt{15^2-9^2}\)
3) \(\sqrt{46-6\sqrt{5}}-\sqrt{46+6\sqrt{5}}\)
4)\(\sqrt{21+6\sqrt{6}}-\sqrt{21-6\sqrt{6}}\)
5) \(\left(2+\sqrt{5}\right).\sqrt{9-4\sqrt{5}}\)
6)\(\left(3-\sqrt{2}\right).\sqrt{7+4\sqrt{3}}\)
7)\(\left(\sqrt{3}+\sqrt{5}\right).\sqrt{7-2\sqrt{10}}\)
8)\(\left(\sqrt{6}+\sqrt{10}\right).\sqrt{4-\sqrt{15}}\)
9) \(\sqrt{2}.\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)
10) \(\sqrt{2}\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\)
11) \(\sqrt{3}-\sqrt{2}-\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)
12) \(\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right).\sqrt{2}+2\sqrt{5}\)
