\(\left(\sqrt{7}+\sqrt{2}\right)^2-2\sqrt{14}\)
= \([\left(\sqrt{7}\right)^2+2\sqrt{7}.\sqrt{2}+\left(\sqrt{2}\right)^2]-2\sqrt{14}\)
= \(\left(7+2\sqrt{14}+2\right)\) \(-2\sqrt{14}\)
= \(9+2\sqrt{14}-2\sqrt{14}\)
= 9
\(\dfrac{\sqrt{14}-7\sqrt{7}}{7-\sqrt{2}}-\dfrac{18}{\sqrt{7}-5}\)
rút gọn biểu thức (3\(\sqrt{2}\)-\(\sqrt{8}+\sqrt{14}\))\(\sqrt{2}-\sqrt{7}\)
rút gọn :
a ) \(\sqrt{2}.\sqrt{7-3\sqrt{5}}\)
b) \(\sqrt{\dfrac{59}{25}+\dfrac{6}{5}\sqrt{2}}\)
c) \(2.\left(\sqrt{10}-\sqrt{2}\right).\sqrt{4+\sqrt{6-2\sqrt{5}}}\)
d) \(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
Hãy rút gọn các biểu thức trong các bài sau đây:
a) \(A=\sqrt{8+7\sqrt{7}}-\sqrt{7}\)
b) \(B=\sqrt{7+4\sqrt{3}}-2\sqrt{3}\)
c) \(C=\sqrt{14-2\sqrt{13}}+\sqrt{14+2\sqrt{13}}\)
d) \(D=\sqrt{22-2\sqrt{21}}-\sqrt{22+2\sqrt{21}}\)
Tính:
\(\left(\sqrt{14}-\sqrt{2}\right)\sqrt{4+\sqrt{7}}\)
\(\left(\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right)\):\(\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
1, Rút gọn biểu thức số:
a, (4+\(\sqrt{7}\)) (\(\sqrt{14}-\sqrt{2}\)) \(\sqrt{4-\sqrt{7}}\)
b, \(\dfrac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4+\sqrt{7}}}\) + \(\dfrac{4-\sqrt{7}}{3\sqrt{2}-\sqrt{4-\sqrt{7}}}\)
tính giá trị biểu thức :
a, \(\left(\sqrt{28}+2\sqrt{14}+\sqrt{7}\right)\sqrt{7}-\left(7+\sqrt{2}\right)^2\)
b, \(\sqrt{\dfrac{5}{2}}+\dfrac{\sqrt{2}}{\sqrt{3}+\sqrt{5}}\)
c, \(\dfrac{8+2\sqrt{15}}{\sqrt{5}+\sqrt{3}}+\dfrac{7-2\sqrt{10}}{\sqrt{5}-\sqrt{2}}\)
d,\(\dfrac{3+4\sqrt{3}}{\sqrt{6}+\sqrt{2}-\sqrt{5}}\)
Rút gọn:
a) \(A=\sqrt{4+2\sqrt{2}}\sqrt{2+2+\sqrt{2}}.\sqrt{2-2+\sqrt{2}}\)
b) \(B=\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right)\sqrt{2}+2\sqrt{5}\)
c) \(C=\left(\sqrt{14}-\sqrt{10}\right)\left(\sqrt{6}+\sqrt{35}\right)\)
d) \(D=\sqrt{11-4\sqrt{7}}-\sqrt{2}.\sqrt{8+3\sqrt{7}}\)
\(\left(\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
