a: \(\sqrt{\left(4+\sqrt2\right)^2}=\left|4+\sqrt2\right|=4+\sqrt2\)
b: \(\sqrt{\left(3-\sqrt5\right)^2}=\left|3-\sqrt5\right|=3-\sqrt5\)
c: \(\sqrt{\left(2\sqrt3-13\right)^2}=\left|2\sqrt3-13\right|=13-2\sqrt3\)
d: \(\sqrt{4x^2}-3x\)
\(=\sqrt{\left(2x\right)^2}-3x\)
=|2x|-3x
=-2x-3x(Vì x<0)
=-5x
e: \(\sqrt{x^2-6x+9}+x-3\)
\(=\sqrt{\left(x-3\right)^2}+x-3\)
=|x-3|+x-3
=x-3+x-3(x>=3)
=2x-6
f: \(A=\sqrt{4x^2-4x+1}+1-2x\)
\(=\sqrt{\left(2x-1\right)^2}+1-2x\)
=|2x-1|+1-2x
TH1: x>=1/2
=>2x-1>=0
=>A=2x-1+1-2x=0
TH2: x<1/2
=>2x-1<0
=>A=1-2x+1-2x=2-4x
h: \(6-2x-\sqrt{9-6x+x^2}\)
\(=6-2x-\sqrt{\left(x-3\right)^2}\)
=6-2x-|x-3|
=6-2x-(3-x)(x<3)
=6-2x-3+x=-x+3
