Đặt:
\(A=\sqrt{9-\sqrt{17}}+\sqrt{9+\sqrt{17}}\)
\(A^2=9-\sqrt{17}+2\sqrt{\left(9-\sqrt{17}\right)\left(9+\sqrt{17}\right)}+9+\sqrt{17}=18+2\sqrt{81-17}=18+2\sqrt{64}=18+2\cdot8=18+16=34\)
=> A = \(\sqrt{34}\)
Chứng minh :
a) \(\sqrt{9-\sqrt{17}}.\sqrt{9+\sqrt{17}}=8\)
b) \(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}=9\)
a, \(\sqrt{9-\sqrt{ }17}\)x \(\sqrt{9+\sqrt{ }17}\)
b, \(\sqrt{7+4\sqrt{ }3}\)
Chứng minh
a)\(\sqrt{9-\sqrt{17}}\cdot\sqrt{9+\sqrt{17}}=8\)
b)(\(\dfrac{1}{5-2\sqrt{6}}+\dfrac{2}{5+2\sqrt{6}}\)
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)\(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}=9\)
B1:Tính
a) \(\sqrt{11}.\sqrt{1100}\)
b) \(\frac{\sqrt{10}-\sqrt{15}}{\sqrt{8}-\sqrt{12}}\)
c) \(\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\)
d) \(\sqrt{9-\sqrt{17}}.\sqrt{9+\sqrt{17}}\)
e) \((\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}})^2\)
Mn giúp mình với ạ!!!
Rút gọn
\(\sqrt{9-\sqrt{17}}.\sqrt{9+\sqrt{18}}\)
\(\left(\frac{1}{5-2\sqrt{6}}+\frac{2}{5+2\sqrt{6}}\right).\left(15+2\sqrt{6}\right)\)
1. Rút gọn: \(\sqrt{17-4\sqrt{9+4\sqrt{7}}}\)
Rút gọn căn thức sau:
\(\sqrt{17+12\sqrt{2}}\) +\(\sqrt{9+4\sqrt{2}}\)
Rút gọn
\(\left(\sqrt{5}+2\right).\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
Mọi người giúp mình với ạ. Xin cảm ơn mọi người!
