\(\left(11-6\sqrt{2}\right)^2=11^2-2.11.6\sqrt{2}+\left(6\sqrt{2}\right)^2=121-132\sqrt{2}+72=193-132\sqrt{2}=VT\)
Vậy biểu thức đã được chứng minh
khai phương hoặc rút gọn biểu thức \(\left(\sqrt{22}-\sqrt{2}\right).\left(6+\sqrt{11}\right).\sqrt{6-\sqrt{11}}\)
B1: rút gọn:
a, \(\sqrt{4-2\sqrt{3}}-\sqrt{3}\)
b, \(\sqrt{11+6\sqrt[]{2}}-3+\sqrt{2}\)
c, \(x-4+\sqrt{16-8x+x^2}\) với x > 4
d, \(\dfrac{x^2-5}{x+\sqrt{5}}\) x khác \(-\sqrt{5}\)
e, \(\dfrac{x^2+2\sqrt{2}x+2}{x+\sqrt{2}}\) x khác \(-\sqrt{2}\)
g, \(\dfrac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\)
giúp em với ạ , em cảm ơn 
Rút gọn:
a) \(\sqrt{5+2\sqrt{6}+\sqrt{14-4\sqrt{6}}}\)
b) \(\sqrt{5-2\sqrt{6}}+\sqrt{11-4\sqrt{6}}\)
c) \(\sqrt{23+6\sqrt{10}}+\sqrt{47+6\sqrt{10}}\)
d) \(\sqrt{21-6\sqrt{10}}+\sqrt{21+6\sqrt{10}}\)
Thực hiện phép tính:
a) \(\left(2\sqrt{2}-\sqrt{3}\right)^2\)
b) \(\left(1+\sqrt{3}-\sqrt{2}\right)\left(1+\sqrt{3}+\sqrt{2}\right)\)
c) \(\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)^2\)
d) \(\left(\sqrt{\sqrt{11}+\sqrt{7}}-\sqrt{\sqrt{11}-\sqrt{7}}\right)^2\)
e) \(\sqrt{2+\sqrt{3}}-\sqrt{2-\sqrt{3}}\)
f) \(\sqrt{21-12\sqrt{3}}-\sqrt{3}\)
g) (\(\sqrt{6}+\sqrt{2}\))(\(\sqrt{3}-2\))\(\sqrt{\sqrt{3}+2}\)
h) \(\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}\)
Mọi người làm giúp em gấp với !!!!!!!!!!!!!!!!!
Chứng minh: \(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}=9\)
Bài 1 : Rút gọn
a) \(\frac{\sqrt{6}+\sqrt{16}}{2\sqrt{3}+\sqrt{28}}\)
b) \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3+\sqrt{4}}}\)
Bài 2: Chứng minh
a)\(\sqrt{9-\sqrt{17}}-\sqrt{9+\sqrt{17}}=8\)
b)\(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}=9\)
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) \(\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right).\sqrt{2}+2\sqrt{5}\)
Chứng minh
a)\(\sqrt{9-\sqrt{17}}\cdot\sqrt{9+\sqrt{17}}=8\)
b)(\(\dfrac{1}{5-2\sqrt{6}}+\dfrac{2}{5+2\sqrt{6}}\)
Rút gọn biểu thức
A. (2-√3)\(\sqrt{7+4\sqrt{3}}\)
B. \(\sqrt{13+4\sqrt{10}}\:+\:\sqrt[]{13-4\sqrt{10}}\)
C.(3 - √2) \(\sqrt{11+6\sqrt{2}}\)
D. (√5+√7) \(\sqrt{12-2\sqrt{35}}\)
E. (√2-√9)\(\sqrt{11+2\sqrt{18}}\)
F. \(\sqrt{46-6\sqrt{5}}\:+\:\sqrt{29-12\sqrt{5}}\)
G.\(\sqrt{49-5\sqrt{96}}\:+\:\sqrt{49+5\sqrt{96}}\)
H.\(\sqrt{13-\sqrt{160\:\:\:\:}}\:+\:\sqrt{53+4\sqrt{90}}\)
