a,
$\sqrt{9x^2-12x+4}-9x+1$
$=\sqrt{(3x-2)^2}-9x+1$
$=|3x-2|-9x+1$
$=|3.\dfrac{1}{3}-2|-9.\dfrac{1}{3}+1$
$=-1$
b,
$\sqrt{10x^2-12\sqrt{10}x+36}$
$=\sqrt{(\sqrt{10}x)^2-2.6.\sqrt{10}x+6^2}$
$=|\sqrt{10}x-6|$ (*)
$x=\dfrac{\sqrt5}{\sqrt2}+\dfrac{\sqrt2}{5}=\dfrac{5+2}{\sqrt2.\sqrt5}=\dfrac{7}{\sqrt{10}}$
$\Rightarrow (*)=1$
c,
$\sqrt{9x^4-24x^2+16}-\sqrt{x^4-8x^2+16}$
$=\sqrt{(3x^2-4)^2}-\sqrt{(x^2-4)^2}$
$=|3x^2-4|-|x^2-4|$
$=|3.3-4|-|3-4|$
$=4$
d,
$\sqrt{3x^2-4\sqrt3 x+4}$
$=|\sqrt3 x-2|$ (*)
$x=\dfrac{3-2}{\sqrt3}=\dfrac{1}{\sqrt3}$
$\Rightarrow (*) =1$
