\(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right)\sqrt{7}+7\sqrt{8}=\left(2\sqrt{7}-2\sqrt{2}\sqrt{7}+\sqrt{7}\right)\sqrt{7}+7\sqrt{8}=2.7-2\sqrt{2}.7+7+14\sqrt{2}=21-14\sqrt{2}+14\sqrt{2}=21\)
Tính GTBT chứa căn:
a,\(\dfrac{2}{4-3\sqrt{2}}\)-\(\dfrac{2}{4+3\sqrt{2}}\)
b,\(\dfrac{2}{1+\sqrt{2}}\)+\(\dfrac{2}{1-\sqrt{2}}\)
c,\(\left(\sqrt{14}-3\sqrt{2}\right)^2+6\sqrt{28}\)
d,\(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right).\sqrt{7}+7\sqrt{8}\)
e,\(\left(\sqrt{6}-\sqrt{5}\right)^2-2\sqrt{120}\)
Chứng minh đẳng thức A = √28 - √7 + √2 × √8-3√7 = 3
\(\sqrt{ }\)9+2[(\(\sqrt{ }\)28-7\(\sqrt{ }\)7)-(\(\sqrt{ }\)28+7\(\sqrt{ }\)7)]
tính giá trị biểu thức :
a) \(\sqrt{8+2\sqrt{7}}-\sqrt{7}\)
b) \(\sqrt{7+4\sqrt{3}}-2\sqrt{3}\)
c) \(\sqrt{14-2\sqrt{13}}+\sqrt{14+2\sqrt{13}}\)
d) \(\sqrt{22-2\sqrt{21}-\sqrt{22+2\sqrt{21}}}\)
tính
a/ (\(\sqrt{2006}\)- \(\sqrt{2005}\)).(\(\sqrt{2006}\)+ \(\sqrt{2005}\))
b/ (\(\frac{1}{7-4\sqrt{3}}\)+ \(\frac{2}{7+4\sqrt{3}}\)).(21+4\(\sqrt{3}\))
c/ \(3\sqrt{\frac{9}{8}}\)- \(\sqrt{\frac{49}{2}}\)+ \(\sqrt{\frac{25}{18}}\)
d/ ( \(5\sqrt{28}-2\sqrt{63}+3\sqrt{112}\)) : \(\sqrt{7}\)
e/ \(\left(\sqrt{5}+\sqrt{3}\right)\sqrt{8-2\sqrt{15}}\)
f/ (\(\frac{4\sqrt{21}-4\sqrt{15}-\sqrt{14}+\sqrt{10}}{4\sqrt{6}-2+4\sqrt{15}-\sqrt{10}}\)
tính
a/ (\(\sqrt{2006}\)- \(\sqrt{2005}\)).(\(\sqrt{2006}\)+ \(\sqrt{2005}\))
b/ (\(\frac{1}{7-4\sqrt{3}}\)+ \(\frac{2}{7+4\sqrt{3}}\)).(21+4\(\sqrt{3}\))
c/ \(3\sqrt{\frac{9}{8}}\)- \(\sqrt{\frac{49}{2}}\)+ \(\sqrt{\frac{25}{18}}\)
d/ ( \(5\sqrt{28}-2\sqrt{63}+3\sqrt{112}\)) : \(\sqrt{7}\)
e/ \(\left(\sqrt{5}+\sqrt{3}\right)\sqrt{8-2\sqrt{15}}\)
f/ (\(\frac{4\sqrt{21}-4\sqrt{15}-\sqrt{14}+\sqrt{10}}{4\sqrt{6}-2+4\sqrt{15}-\sqrt{10}}\)
Rút gọn
A= căn 8+ 2 căn 7 trừ căn 8- 2 căn 7
\(\sqrt{8-2\sqrt{7}}+\sqrt{23-8\sqrt{7}}\)
Rút gọn các biểu thức sau
a. √5- √(1+ √5)
b. √(2-√3)^2 +√3
c√(√7 -3)/^2+ √7
d.√(√8-7)^2 +√8
e.√(√2 -√7)^2 +√2
