a: \(\sqrt{\left(\sqrt5-2\right)^2}-\sqrt{\left(3-\sqrt5\right)^2}+\sqrt{\left(\sqrt2-\sqrt5\right)^2}-\sqrt{\left(\sqrt2+3\right)^2}-\sqrt{45}+\sqrt{1\frac13}\)
\(=\sqrt5-2-\left|3-\sqrt5\right|+\sqrt5-\sqrt2-\left|3+\sqrt2\right|-3\sqrt5+\sqrt{\frac43}\)
\(=-\sqrt5-2-\sqrt2-3+\sqrt5-3-\sqrt2+\frac{2}{\sqrt3}=-2\sqrt2-8+\frac{2\sqrt3}{3}\)
b: \(\sqrt{7+2\sqrt6}-\sqrt{3-2\sqrt2}-\sqrt{5-2\sqrt6}\)
\(=\sqrt{\left(\sqrt6+1\right)^2}-\sqrt{\left(\sqrt2-1\right)^2}-\sqrt{\left(\sqrt3-\sqrt2\right)^2}\)
\(=\sqrt6+1-\sqrt2+1-\sqrt3+\sqrt2=\sqrt6-\sqrt3+2\)
c:Đặt A= \(\sqrt{a^2-6a+9}-\sqrt{a^2+2a+1}\)
\(=\sqrt{\left(a-3\right)^2}-\sqrt{\left(a+1\right)^2}\)
=|a-3|-|a+1|
Th1: a<-1
=>a+1<0; a-3<0
=>A=3-a-(-a-1)
=3-a+a+1
=4
TH2: -1<=a<3
=>a+1>=0; a-3<0
=>A=3-a-(a+1)=3-a-a-1=-2a+2
TH3: a>=3
=>a+1>0; a-3>=0
=>A=a-3-(a+1)=a-3-a-1
=-4
