A fundamental and oft'-overlooked principle of Real Numbers is missing.

sqrt(x^2) = |x| in the absence of additional information about 'x'.

If you KNOW x >= 0, then sqrt(x^2) = x.

If you do not KNOW x >= 0, then sqrt(x^2) = |x|

These are correct:

(x^6)^(1/2) = |x^3| -- x^3 could be positive or negative.

(x^8)^(1/2) = x^4 -- x^4 cannot be negative.

sqrt(25) = 5 -- 5 > 0

This makes your #1 a little off.

#2 is easier, since cube roots don't do the same thing as even roots.

#3 is OK, but it may have been luck.