Lời giải:
\(\frac{18}{2\sqrt{3}-\sqrt{6}}=\frac{18(2\sqrt{3}+\sqrt{6})}{(2\sqrt{3}-\sqrt{6})(2\sqrt{3}+\sqrt{6})}=\frac{36\sqrt{3}+18\sqrt{6}}{6}\)
\(=6\sqrt{3}+3\sqrt{6}\)
$\Rightarrow a=6; b=-3$
$\Rightarrow a+b=6+(-3)=3$
Rút gọn:
a)\(\dfrac{\sqrt{a}+a\sqrt{b}-\sqrt{b}-b\sqrt{a}}{ab-1}\)
b) \(\dfrac{2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3}{2\sqrt{5}-2\sqrt{10}-\sqrt{3}+\sqrt{6}}\)
Rút gọn các biểu thức sau :
a,\(\dfrac{\sqrt{6}+\sqrt{10}}{\sqrt{21}+\sqrt{35}}\)
b,\(\dfrac{\sqrt{405}+3\sqrt{27}}{3\sqrt{3}+\sqrt{45}}\)
c,\(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}-\sqrt{6}-\sqrt{9}-\sqrt{12}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
d, D=\(\dfrac{2}{x^2-y^2}\cdot\sqrt{\dfrac{9\left(x^2+2xy+y^2\right)}{4}}\) \(\left(vớix\ne y,x\ne-y\right)\)
Rút gọn :
a) \(\dfrac{3\sqrt{2-6}}{\sqrt{2-1}}\)
b) \(\dfrac{3\sqrt{5}+5\sqrt{3}}{\sqrt{3}+\sqrt{5}}\)
c) \(\dfrac{x-y}{\sqrt{x}-\sqrt{y}}\)
A)\(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
B)\(\left(\sqrt{2}+1^{ }\right)^3-\left(\sqrt{2}-1\right)^3\) C)\(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\) D)\(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}\) E)\(\dfrac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\) F)\(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
Rút gọn :
a) \(\dfrac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\)
b) \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
Rút gọn:
a)\(\dfrac{\sqrt{6}+\sqrt{10}}{\sqrt{21}+\sqrt{35}}\)
b)\(\dfrac{\sqrt{405}+3\sqrt{27}}{3\sqrt{3}+\sqrt{45}}\)
c)\(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}-\sqrt{6}-\sqrt{9}-\sqrt{12}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
d)\(\dfrac{\sqrt{6-2\sqrt{5}}}{\sqrt{5}-1}\)
BÀI 1 : THỰC HIỆN PHÉP TÍNH
a, \(\left(1+\sqrt{3}-\sqrt[2]{2}\right)\times\left(1+\sqrt{3}+\sqrt[2]{2}\right)\)
b, \(\left(\dfrac{3}{2}\times\sqrt{6}+2\times\sqrt{\dfrac{2}{3}}-4\times\sqrt{\dfrac{3}{2}}\right)\times\left(3\times\sqrt{\dfrac{2}{3}}-\sqrt{12}-\sqrt{6}\right)\)
BÀI 2 : rút gọn
B = \(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-2}}\)
a. \(\sqrt{21+6\sqrt{6}}+\sqrt{9+2\sqrt{18}}-2\sqrt{6+3\sqrt{3}}\)
b. \(\sqrt{6+2\sqrt{2\sqrt{3-\sqrt{4+2\sqrt{3}}}}}\)
c. \(\sqrt{4+\sqrt{15}}-\sqrt{7-3\sqrt{5}}\)
d.\(\sqrt{2+\sqrt{3}}-\sqrt{2-\sqrt{3}}\)
e. \(\sqrt{\frac{9}{4}-\sqrt{2}}+\sqrt{2}\)
bài 1: tính
a) \(\sqrt{1,2\cdot27}\) b) \(\sqrt{55\cdot77\cdot35}\)
c) (\(\sqrt{3}-\sqrt{2}\) )\(^2\) d) (3\(\sqrt{2}-1\))*(3\(\sqrt{2}+1\))
e) (\(\sqrt{6}+7\)) (\(\sqrt{3}-\sqrt{2}\)) i) \(\sqrt{\dfrac{1}{8}}\cdot\sqrt{2}\cdot\sqrt{125}\cdot\sqrt{\dfrac{1}{5}}\)
h) \(\sqrt{\sqrt{2}-1}\cdot\sqrt{\sqrt{2}}+1\)
bài 2: tính
a) \(\sqrt{9}-\sqrt{17}\cdot\sqrt{9}+\sqrt{17}\)
b) 2\(\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}\)
c) \(\dfrac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\) d) \(\dfrac{\sqrt{10}+\sqrt{15}}{\sqrt{8}+\sqrt{12}}\)
e) \(\dfrac{\sqrt{15}-\sqrt{6}}{\sqrt{35}-\sqrt{14}}\) f) \(\dfrac{x+\sqrt{xy}}{9+\sqrt{xy}}\) (xy>0)
