Degree of polynomial :$ [x + (x^3 – 1)^{1/2}]^5 + [x – (x^3 – 1)^{1/2}]^5 $ What is the degree of the polynomial of the following expression ?
$$ [x + (x^3 – 1)^{1/2}]^5 + [x – (x^3 – 1)^{1/2}]^5 $$
If I am not very wrong the highest power of x is  $\frac {15}{2} $ ?! So the degree is floor(15/2) = 7 ?! The answer is 7 but I am not sure of this approach.
Please comment.

If you expand the 5th powers, the terms that have square roots in them will cancel.
