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\(a,\frac{\sqrt{108x^3}}{\sqrt{12x}}=\frac{\sqrt{36.3.x^3}}{\sqrt{3.4.x}}=\frac{6\sqrt{3}.\sqrt{x}^3}{2\sqrt{3}.\sqrt{x}}=3\sqrt{x}^2=3x\)
\(b,\frac{\sqrt{13x^4y^6}}{\sqrt{208x^6y^6}}=\frac{\sqrt{13}.\sqrt{x^4}.\sqrt{y^6}}{\sqrt{16.13}.\sqrt{x^6}.\sqrt{y^6}}=\frac{\sqrt{13}.x^2y^3}{4\sqrt{13}x^3y^3}=\frac{1}{4x}\)
\(c,\frac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}-\left(\sqrt{x}+\sqrt{y}\right)^2\)
\(=\frac{\sqrt{x}^3+\sqrt{y}^3}{\sqrt{x}+\sqrt{y}}-\left(x+2\sqrt{xy}+y\right)\)
\(=\frac{\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)}{\sqrt{x}+\sqrt{y}}-x-2\sqrt{xy}-y\)
\(=x-\sqrt{xy}+y-x-2\sqrt{xy}-y=-3\sqrt{xy}\)
\(d,\sqrt{\frac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}}=\frac{\sqrt{\left(\sqrt{x}-1\right)^2}}{\sqrt{\left(\sqrt{x}+1\right)^2}}=\frac{\sqrt{x}-1}{\sqrt{x}+1}\)
Đk chỗ này là \(\sqrt{x}-1\ge0\Rightarrow\sqrt{x}\ge\sqrt{1}\Rightarrow x\ge1\)nhé
\(e,\frac{x-1}{\sqrt{y}-1}.\sqrt{\frac{\left(y-2\sqrt{y}+1\right)^2}{\left(x-1\right)^4}}=\frac{x-1}{\sqrt{y}-1}.\frac{y-2\sqrt{y}+1}{\left(x-1\right)^2}\)
\(=\frac{\left(x-1\right)\left(\sqrt{y}-1\right)^2}{\left(\sqrt{y}-1\right)\left(x-1\right)^2}=\frac{\sqrt{y}-1}{x-1}\)
a. Ta có:\(\frac{x}{y}\sqrt{\frac{y^2}{x^4}=}\) \(\frac{x}{y}.\frac{\left|y\right|}{x^2}=\frac{x.y}{x^2y}\)\(=\frac{1}{x}\)(Vì \(x\ne0;y>0\))
b \(3x^2\sqrt{\frac{8}{x^2}}=3x^2\frac{2\sqrt{2}}{\left|x\right|}=\frac{6x^2\sqrt{2}}{-x}=-6x\sqrt{2}\)( Vì \(x< 0\))
a) \(\frac{\sqrt{4mn^2}}{\sqrt{20m}}=\sqrt{\frac{4mn^2}{20m}}=\sqrt{\frac{n^2}{5}}=\frac{n}{\sqrt{5}}\)
b) \(\frac{\sqrt{16a^4b^6}}{\sqrt{12a^6b^6}}=\sqrt{\frac{16a^4b^6}{12a^6b^6}}=\sqrt{\frac{4}{3a^2}}=\frac{2}{\sqrt{3}.\left|a\right|}=-\frac{2}{a\sqrt{3}}\)
d) \(\frac{x\sqrt{x}-y\sqrt{y}}{\sqrt{x}-\sqrt{y}}=\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)}{\sqrt{x}-\sqrt{y}}=x+\sqrt{xy}+y\)
e) \(\sqrt{\frac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}}=\sqrt{\frac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}+1\right)^2}}=\frac{\left|\sqrt{x}-1\right|}{\sqrt{x}+1}\)
\(A=\left(\sqrt{6\left(x^2-2xy^2+y^3\right)}+\sqrt{6.4x^2y}\right).\frac{1}{\sqrt{6y}}\)
\(=\left(\sqrt{6\left(x^2-xy^2+y^3\right)}+2x\sqrt{6y}\right).\frac{1}{\sqrt{6y}}\)
\(=\left[\sqrt{6}\left(\sqrt{x^2-xy^2+y^3}+2x\sqrt{y}\right)\right].\frac{1}{\sqrt{6y}}=\sqrt{6}\left(\sqrt{x^2-xy^2+y^3}-2x\sqrt{y}\right).\frac{1}{\sqrt{6}\sqrt{y}}\)
\(=\frac{x^2-xy^2+y^3}{\sqrt{y}}-\frac{2x\sqrt{y}}{\sqrt{y}}=\frac{x^2-xy^2+y^3}{\sqrt{y}}-2x\)
mik chỉ lm đến đây đc thui
a) \(A=\left(\sqrt{6}+\sqrt{10}\right).\left(\sqrt{5}-\sqrt{3}\right)\)
\(=\sqrt{2}\left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{5}-\sqrt{3}\right)\)
\(=2\sqrt{2}\)
\(B=\frac{1}{\sqrt{x}-2}-\frac{1}{\sqrt{x}+2}+1\)
\(=\frac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{\sqrt{x}-2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}+1\)
\(=\frac{4}{x-4}+1\)
\(=\frac{4}{x-4}+\frac{x-4}{x-4}=\frac{x}{x-4}\)
\(\left[\frac{2}{3\sqrt{x}}-\frac{2}{\sqrt{x}+1}.\left(\frac{\sqrt{x}+1}{3\sqrt{x}}-\sqrt{x}-1\right)\right]:\frac{\sqrt{x}-1}{\sqrt{x}}\)
\(=\left[\frac{2}{3\sqrt{x}}-\frac{2}{\sqrt{x}+1}.\left(\frac{\sqrt{x}+1-3x-3\sqrt{x}}{3\sqrt{x}}\right)\right].\frac{\sqrt{x}}{\sqrt{x}-1}\)
\(=\left[\frac{2}{3\sqrt{x}}-\frac{2}{\sqrt{x}+1}.\frac{-3x-2\sqrt{x}+1}{3\sqrt{x}}\right].\frac{\sqrt{x}}{\sqrt{x}-1}\)
\(=\left[\frac{2}{3\sqrt{x}}-\frac{2}{\sqrt{x}+1}.\frac{\left(\sqrt{x}+1\right)\left(-3\sqrt{x}+1\right)}{3\sqrt{x}}\right].\frac{\sqrt{x}}{\sqrt{x}-1}\)
\(=\left[\frac{2}{3\sqrt{x}}-\frac{-6\sqrt{x}+2}{3\sqrt{x}}\right].\frac{\sqrt{x}}{\sqrt{x}-1}\)
\(=\frac{2\sqrt{x}}{\sqrt{x}-1}\)
a. \(\sqrt{\dfrac{63y^3}{7y}}\)=\(\sqrt{9y^2}\)=3y
b.\(\sqrt{\dfrac{48x^3}{3x^5}}\)=\(\sqrt{16\cdot\dfrac{1}{X^2}}\)= \(\sqrt{16}\cdot\sqrt{\dfrac{1}{X^2}}\)=\(4\cdot\dfrac{1}{X}=\dfrac{4}{X}\)
c.\(\sqrt{\dfrac{45mn^2}{20m}}=\sqrt{\dfrac{9n^2}{4}}=\dfrac{\sqrt{9n^2}}{\sqrt{4}}=\dfrac{3n}{2}\)
d. \(\sqrt{\dfrac{16a^4b^6}{128a^6b^6}}=\sqrt{\dfrac{1}{8a^2}}=\dfrac{1}{2\sqrt{2}a}\)
a) \(\dfrac{\sqrt{63y^3}}{\sqrt{7y}}=\sqrt{\dfrac{63y^3}{7y}}=\sqrt{9y^2}=3y\)
b) \(\dfrac{\sqrt{48x^3}}{\sqrt{3x^5}}=\sqrt{\dfrac{48x^3}{3x^5}}=\sqrt{\dfrac{16}{x^2}}=\dfrac{4}{x}\)
c) \(\dfrac{\sqrt{45mn^2}}{\sqrt{20m}}=\sqrt{\dfrac{45mn^2}{20m}}=\sqrt{\dfrac{9n^2}{4}}=\dfrac{3n}{2}\)
d) \(\dfrac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}=\sqrt{\dfrac{16a^4b^6}{128a^6b^6}}=\sqrt{\dfrac{1}{8a^2}}=\dfrac{1}{2\left|a\right|\sqrt{2}}=\dfrac{-1}{2a\sqrt{2}}\)
\(\frac{\sqrt{108x^3}}{\sqrt{12x}}=\sqrt{\frac{108x^3}{12x}}=\sqrt{9x^2}=3x\)( vì \(x>0\))
\(\frac{\sqrt{13x^4y^6}}{\sqrt{208x^6y^6}}=\sqrt{\frac{13x^4y^6}{208x^6y^6}}=\sqrt{\frac{1}{16x^2}}=\left|\frac{1}{4x}\right|=\frac{-1}{4x}\)( vì \(x< 0\))