\(a,\sqrt{\left(\sqrt{2}-3\right)^2}-\sqrt{11-6\sqrt{2}}\\ =\left|\sqrt{2}-3\right|-\sqrt{\left(3-\sqrt{2}\right)^2}\\ =3-\sqrt{2}-\left|3-\sqrt{2}\right|\\ =3-\sqrt{2}-3+\sqrt{2}\\ =0\)
\(b,\dfrac{2}{2a-1}\sqrt{\dfrac{4a^2\left(1-4a+4a^2\right)}{16}}\left(dk:a< 0\right)\)
\(=\dfrac{2}{2a-1}.\dfrac{\sqrt{2^2}.\sqrt{a^2}.\sqrt{\left(1-2a\right)^2}}{\sqrt{4^2}}\)
\(=\dfrac{2}{2a-1}.\dfrac{2.\left|a\right|.\left|1-2a\right|}{4}\)
\(=\dfrac{-a.\left(-1+2a\right)}{2a-1}\)
\(=-a\)
\(c,x^3y^2.\sqrt{\dfrac{3x^3y}{4}}.\sqrt{\dfrac{36}{3xy^3}}\left(dk:y< 0,x>0\right)\)
\(=x^3y^2.\sqrt{\dfrac{108x^3y}{12xy^3}}\)
\(=x^3y^2.\sqrt{\dfrac{9x^2}{y^2}}\)
\(=x^3y^2.\dfrac{\sqrt{3^2}.\sqrt{x^2}}{\sqrt{y^2}}\)
\(=x^3y^2.\dfrac{3.\left|x\right|}{\left|y\right|}\)
\(=x^3y^2.\dfrac{3x}{-y}\)
\(=-3x^4y\)
\(d,5x^3y^2\sqrt{\dfrac{12xy^3}{75xy^5}}\left(dk:y< 0\right)\\ =5x^3y^2\sqrt{\dfrac{4}{25y^2}}\)
\(=5x^3y^2.\dfrac{\sqrt{2^2}}{\sqrt{5^2}.\sqrt{y^2}}\)
\(=5x^3y^2.\dfrac{2}{5.\left|y\right|}\)
\(=-2x^3y\)
a: \(=3-\sqrt{2}-3+\sqrt{2}=0\)
b: \(=\dfrac{2}{2a-1}\cdot\dfrac{1}{2}\cdot\dfrac{\left|2a-1\right|}{1}\)
\(=\dfrac{1}{2a-1}\cdot\dfrac{-\left(2a-1\right)}{1}=-1\)
c: \(=x^3y^2\cdot\sqrt{\dfrac{3x^3y}{3xy^3}\cdot\dfrac{36}{4}}\)
\(=x^3y^2\cdot3\cdot\sqrt{\dfrac{x^2}{y^2}}\)
\(=3x^3y^2\cdot\dfrac{-x}{y}=-3x^4y\)
d: \(=5x^3y^2\cdot\sqrt{\dfrac{4}{25y^2}}=5x^3y^2\cdot\dfrac{2}{5}\cdot\dfrac{-1}{y}=-2x^3y\)
