Rút gọn
a)\(3\sqrt{40\sqrt{12}}+4\sqrt{\sqrt{75}}-5\)\(\sqrt{5\sqrt{48}}\)
b)\(\sqrt{8\sqrt{3}}+3\sqrt{20\sqrt{3}}-2\sqrt{45\sqrt{3}}\)
c)\(\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)\left(x\ge0;y\ge0\right)\)
d)\(\left(\sqrt{x}+1\right)\left(x+1-\sqrt{x}\right)\left(x\ge0;y\ge0\right)\)
e)\(\left(\sqrt{x}+y\right).\left(x+y^2-y\sqrt{2}\right)\left(x\ge0;y\ge0\right)\)
Rút gọn:
a)\(2\sqrt{3x}-4\sqrt{3x}\)+\(27-2\sqrt{3x}\)(\(x\ge0\))
b)\(3\sqrt{2x}-5\sqrt{8x}\)+\(7\sqrt{8x}+28\)\(\left(x\ge0\right)\)
c)\(\frac{2}{x^2-y^2}\sqrt{\frac{3\left(x+y\right)^2}{2}}\)\(\left(x\ge0,y\ge0,x\ne y\right)\)
d)\(\frac{2}{2a-1}\sqrt{5a^2\left(1-4a+4a^2\right)}\)
rút gọn \(\frac{2}{x^2y^2}\sqrt{\frac{3\left(x+y\right)^2}{2}}\left(x\ge0;y\ge0;x\ne y\right)\)
a)\(3\sqrt{40\sqrt{12}}+4\sqrt{\sqrt{75}}-5\)\(\sqrt{5\sqrt{48}}\)
b)\(\sqrt{8\sqrt{3}}+3\sqrt{20\sqrt{3}}-2\sqrt{45\sqrt{3}}\)
c)\(\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)\left(x\ge0;y\ge0\right)\)
d)\(\left(\sqrt{x}+1\right)\left(x+1-\sqrt{x}\right)\left(x\ge0;y\ge0\right)\)
e)\(\left(\sqrt{x}+y\right)\left(x+y^2-y\sqrt{2}\right)\left(x\ge0;y\ge0\right)\)
Cho \(P=\frac{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\div\left(\frac{x-y}{\sqrt{x}-\sqrt{y}}+\frac{x\sqrt{x}-y\sqrt{y}}{y-x}\right)\)Với \(x,y\ge0;x\ne y\)
a) Rút gọn \(P\)
b) CMR: \(P>1\)
Cho A = \(\left(\frac{x-y}{x-\sqrt{y}}-\frac{x\sqrt{x}-y\sqrt{y}}{x-y}\right):\left(\frac{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\right)\)
a) Rút gọn A
b) CM: \(A\ge0\)
B1 Rút gọn
a)\(\sqrt{6+2\sqrt{5}}-\sqrt{29-12\sqrt{2}}\)
b)\(\frac{2}{x^2y^2}\sqrt{\frac{3\left(x+y\right)^2}{2}}\left(x\ge0;y\ge0;x\ne y\right)\)
c)\(\frac{2}{2a-1}\sqrt{5a^2\left(1-4a+4a^2\right)}\left(a>\frac{1}{2}\right)\)
B2 giải pt
\(\sqrt{3-x}+3\sqrt{12-4x}-5\sqrt{48-16x}=-39\)
HELP ME!!!!
Rút gọn:
a,\(\frac{\left(x\sqrt{y}+y\sqrt{x}\right).\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}\left(x,y>0\right)\)
b,\(\frac{\sqrt{x^3}-1}{\sqrt{x}-1}\left(x\ge0;x\ne1\right)\)
c,\(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}\)
Giải giúp mình nha
1/ Thực hiện phép tính
a) \(\sqrt{9-2\sqrt{20}}+\sqrt{12-2\sqrt{35}}\)
b) \(\sqrt{5-\sqrt{21}}-\sqrt{5+\sqrt{21}}\)
2/Rút gọn biểu thức
a) \(\sqrt{\frac{\left(x-2\right)^4}{\left(3-x\right)^2}}+\frac{x^2-1}{x-3}\left(x< 3\right)\)
b) \(4x-\sqrt{8}+\frac{\sqrt{x^3+2x^2}}{\sqrt{x+2}}\left(x>-2\right)\)
3/ Phân tích thành nhân tử
a) \(\sqrt{x}+\sqrt{y}-5\sqrt{xy}-5y\left(x,y\ge0\right)\)
b) \(x\sqrt{x}-y\sqrt{y}\left(x,y\ge0\right)\)
