Which of the following real numbers are algebraic? A real number is said to be algebraic if it is root of a non-zero polynomial with integer coeﬃcients.

Which of the following real numbers are algebraic?
(a) $\cos (\pi/5)$
(b) $e^{\frac{1}{2}\log2}$
(c) $5^{1/7}+7^{1/5}$


(a) I am not sure.
(b) it is algebraic since this is $\sqrt{2}$ and $x^2-2$ is the polynomial.
(c) not sure but I think this is also algebraic and a polynomial og order 35 may be the answer.but I cant prove this.
can I get some help please.
You are correct on (b). 

For (a) and (c), the key facts are that a sum, quotient and product of algebraic numbers are algebraic. (You need to prove this if you haven't yet!) 

$$\cos (\pi/5)=\frac{ \zeta_{10}+\zeta_{10}^{-1}}2$$ where $\zeta_{10}$ is a $10$th root of unity, and (c) is plainly obvious from the key facts.
(c) this is a solution of 35x7 deg polynomial
when we solve :  x-5^(1/7)=7^(1/5)
raising 35 power
x^35 - 5^5 - 7^7 = 5^(1/7)*(polynomial of degree 34)

again raising 7th power we get desired polynomial.

(a) refer wolfram alpha.