Find the result of the root expression, is my answer correct or not? Suppose $a < 0 < b$. Then what is the result of:
$\sqrt{(a-b)^2} + \sqrt[6]{ b^6 } = ?$
I have a solution but I can't be sure if I did a mistake, because I usually do! My solution: 
Call $a = -c$ for some $0 < c $. Then,
$=\sqrt{(-c-b)^2} + \sqrt[6]{ b^6 }$
$=\sqrt{(- (c+b))^2} + \sqrt[6]{ b^6 }$
$=\sqrt{(c+b)^2} + \sqrt[6]{ b^6 }$
$=(c+b) + b$
$= -a +2b$

i would write $$\sqrt{(a-b)^2}+\sqrt[6]{b^6}=\sqrt{(b-a)^2}+\sqrt[6]{b^6}=b-a+b$$
this is the same as you
