Math (Algebra)
posted by Dan on .
A number is called algebraic if there is a polynomial with rational coefficients for which the number is a root. For example,√2 is algebraic because it is a root of the polynomial x^2−2. The number √2+√3+√5 is also algebraic because it is a root of a monic polynomial of degree 8, namely x^8+ax^7+bx^6+cx^5+dx^4+ex^3+fx^2+gx+h. Find a+b+c+d+e+f+g+h.

If the coefficients are all rational, then the irrational roots must occur in conjugate pairs. So, the polynomial is
(x(√2+√3+√5))
(x(√2+√3√5))
(x(√2√3+√5))
(x(√2√3√5))
(x(√2+√3+√5))
(x(√2+√3√5))
(x(√2√3+√5))
(x(√2√3√5))
x^8  40x^6 + 352x^4  960x^2 + 576