anyone mind checking it

1) 3\(\sqrt[6]{3}\) - 2\(\sqrt[6]{192}\) - 6\(\sqrt[6]{320}\) = -3\(\sqrt[6]{3}\) - 4\(\sqrt{3}\) - 2\(\sqrt{5}\) = \(\sqrt[6]{3}\) + 2\(\sqrt{5}\)

2) \(\sqrt[3]{320}\) - 4\(\sqrt[3]{5}\) + 2\(\sqrt[3]{135}\) + 2\(\sqrt[3]{16}\) = -4\(\sqrt{5}\) - 4\(\sqrt[3]{5}\) + 6\(\sqrt{5}\) + 4\(\sqrt{2}\) =
6\(\sqrt[3]{5}\) + 4\(\sqrt{2}\)

3)2\(\sqrt[3]{6}\) - \(\sqrt[6]{6}\) + 3\(\sqrt[3]{6}\)
- 3\(\sqrt[6]{384}\) = 2\(\sqrt[3]{6}\) - \(\sqrt[6]{6}\) + 3\(\sqrt[3]{6}\) - 6\(\sqrt{6}\)

 

You can check the results with a calculator -- or type things in at a python prompt:

>>> 3*3**(1./6) - 2*192**(1./6) - 6*320**(1./6)
-16.89286278731797

(You don't need the decimal points after the 1's if you're using python 3.x.)

Your first problem has an error, as your last expression can't be negative.