\(\left(\sqrt{\sqrt{14}+\sqrt{5}}+\sqrt{\sqrt{14}-\sqrt{5}}\right)^2\)
= \(\left(\sqrt{\sqrt{14}+\sqrt{5}}\right)^2+2\left(\sqrt{\sqrt{14}+\sqrt{5}}\right).\left(\sqrt{\sqrt{14}+\sqrt{5}}\right)+\left(\sqrt{\sqrt{14}+\sqrt{5}}\right)^2\)
= \(\sqrt{14}+\sqrt{5}+2\left(\sqrt{14-5}\right)+\sqrt{14}+\sqrt{5}\)
= \(2\sqrt{14}+2\sqrt{5}+18\)
= 22 + \(2\sqrt{5}\)
\(\left(\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right)\):\(\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
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) \(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
\(\left(\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
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) \(D=\sqrt{11-4\sqrt{7}}-\sqrt{2}.\sqrt{8+3\sqrt{7}}\)
A) \(2\sqrt{3}+\sqrt{48}-\sqrt{75}-\sqrt{243}\)
b) \(\left(\frac{\sqrt{7}-\sqrt{14}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}+\sqrt{5}}\)
c) \(\left(\sqrt{3}+1\right)\sqrt{4-2\sqrt{3}}\)
d) \(5\sqrt{2}+\sqrt{18}-\sqrt{98}-\sqrt{288}\)
e)\(\left(\frac{\sqrt{3}-\sqrt{6}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{3}+\sqrt{5}}\)
g)\(\left(\sqrt{3}-1\right)\sqrt{4+2\sqrt{3}}\)
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 biểu thức
1)\(\sqrt{2-\sqrt{3}}\) nhân \(\left(\sqrt{6}+\sqrt{2}\right)\) nhân \(\left(2+\sqrt{3}\right)\)
2)\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
3)\(\left(\sqrt{9-2\sqrt{14}}+\dfrac{5}{\sqrt{7}-\sqrt{2}}\right)^2\)
mik đag cần gấp bài này
Bài 1: Rút gọn
A=\(\sqrt{7}-4\sqrt{3}+\sqrt{4}-2\sqrt{3}\)
B=\(\left(\frac{2+5-\sqrt{5}}{\sqrt{5}-1}\right)\) \(\left(\frac{2-5+\sqrt{5}}{\sqrt{5}+1}\right)\)
C=\(\left(\sqrt{3}+1\right)\) \(\frac{\sqrt{14}-6\sqrt{3}}{\sqrt{5}+1}\)
Rút gọn pt
a, \(-\dfrac{2}{3}\sqrt{\dfrac{\left(a-b\right)^3.b^5}{c}.\dfrac{9}{4}\sqrt{\dfrac{c^3}{2\left(a-b\right)}}\sqrt{ }98b}\)
b, \(\left(\sqrt{ab}+2\sqrt{\dfrac{b}{a}}-\sqrt{\dfrac{a}{b}+\dfrac{1}{ab}}\right).\sqrt{ab}\)
c, \(\left(\sqrt{b}-3\sqrt{3}+5\sqrt{2}-\dfrac{1}{2}\sqrt{8}\right).2\sqrt{6}\)
d, \(\dfrac{\sqrt{15}-\sqrt{6}}{\sqrt{35}-\sqrt{14}}\)
