Câu a bạn xem lại đề nhé vì \(\sqrt{2-6}=\sqrt{-4}\left(VLý\right)\)
b) \(\dfrac{3\sqrt{5}+5\sqrt{3}}{\sqrt{3}+\sqrt{5}}=\dfrac{\sqrt{3.5}\left(\sqrt{3}+\sqrt{5}\right)}{\sqrt{3}+\sqrt{5}}=\sqrt{15}\)
c) \(\dfrac{x-y}{\sqrt{x}-\sqrt{y}}=\dfrac{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}-\sqrt{y}}=\sqrt{x}+\sqrt{y}\)
bài 1: rút gọn các biểu thức.
a) \(\dfrac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}-(\sqrt{x}-\sqrt{y})^2\)
b) \(\sqrt{\dfrac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}}(x\ge0)\)
c) \(\dfrac{x-1}{\sqrt{y}-1}\sqrt{\dfrac{(y-2\sqrt{y}+1)^2}{(x-1)^4}}(x\ne1,y\ne1,y>0)\)
bài 2:rút gọn và tính.
a) \(\sqrt{\dfrac{\sqrt{a}-1}{\sqrt{b}+1}:}\sqrt{\dfrac{\sqrt{b}-1}{\sqrt{a}+1}với}a=7,25;b=3,25\)
b) \(\sqrt{15a^2-8a\sqrt{15}+16}vớia=\sqrt{\dfrac{3}{5}}+\sqrt{\dfrac{5}{3}}\)
c) \(\sqrt{10a^2-4a\sqrt{10}+4}vớia=\sqrt{\dfrac{2}{5}}+\sqrt{\dfrac{5}{2}}\)
d) \(\sqrt{a^2+2\sqrt{a^2-1}}-\sqrt{a^2-2\sqrt{a^2-1}}(a=\sqrt{5})\)
bài 3: rút gọn các biểu thức.
a) \(\sqrt{9(x-5)^2}(x\ge5)\)
b) \(\sqrt{x^2.(x-2)^2}(x< 0)\)
c)\(\dfrac{\sqrt{108x^3}}{\sqrt{12x}}(x>0)\)
d)\(\dfrac{\sqrt{13x^4y^6}}{\sqrt{208x^6y^6}}(x< 0:y\ne0)\)
ai giúp mik vs ạ, cảm ơn !
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=\(\dfrac{2}{x^2-y^2}\cdot\sqrt{\dfrac{9\left(x^2+2xy+y^2\right)}{4}}\) \(\left(vớix\ne y,x\ne-y\right)\)
B1: rút gọn:
a, \(\sqrt{4-2\sqrt{3}}-\sqrt{3}\)
b, \(\sqrt{11+6\sqrt[]{2}}-3+\sqrt{2}\)
c, \(x-4+\sqrt{16-8x+x^2}\) với x > 4
d, \(\dfrac{x^2-5}{x+\sqrt{5}}\) x khác \(-\sqrt{5}\)
e, \(\dfrac{x^2+2\sqrt{2}x+2}{x+\sqrt{2}}\) x khác \(-\sqrt{2}\)
g, \(\dfrac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\)
giúp em với ạ , em cảm ơn 
Rút gọn:
a)\(\dfrac{\sqrt{a}+a\sqrt{b}-\sqrt{b}-b\sqrt{a}}{ab-1}\)
b) \(\dfrac{2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3}{2\sqrt{5}-2\sqrt{10}-\sqrt{3}+\sqrt{6}}\)
đơn giản biểu thức
a \(\dfrac{3-2\sqrt{2}}{1-\sqrt{2}}\)
b \(\dfrac{x\sqrt{y}-y\sqrt{x}}{x-y}\) (x,y >0)
c \(\dfrac{5\sqrt{16}-\sqrt{15}}{6-2\sqrt{6}}\)
d \(\dfrac{x\sqrt{x}-y\sqrt{y}}{x-y}\) ( x,y>0)
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)\(\dfrac{\sqrt{6-2\sqrt{5}}}{\sqrt{5}-1}\)
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)\(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
Cho \(Q=\left(\dfrac{1}{\sqrt{x}-2}+\dfrac{5\sqrt{x}-4}{2\sqrt{x}-x}\right):\left(\dfrac{2+\sqrt{x}}{\sqrt{x}}-\dfrac{\sqrt{x}}{\sqrt{x}-2}\right)\)
a) Tìm ĐKXĐ và Rút gọn
b) Tìm x khi Q =5
c) Tìm Q khi x=\(\dfrac{3-\sqrt{5}}{2}\)
B2 : Tính :
a, \(\left(\sqrt{x}-3\right)\)\(.\left(\sqrt{x}+2\right)\)
b, \(\left(\sqrt{x}-\sqrt{y}\right).\)\(\left(\sqrt{x}+\sqrt{y}\right)\)
c, \(\left(\sqrt{\dfrac{25}{3}}-\sqrt{\dfrac{49}{3}}+\sqrt{3}\right)\)\(.\sqrt{3}\)
d,\(\left(1+\sqrt{3}-\sqrt{5}\right)\)\(.\left(1+\sqrt{3}+\sqrt{5}\right)\)
