Sanity check answers of minimal polynomials

Question

This question originates from Pinter's Abstract Algebra, Chapter 27, Exercise B1.

Find the minimum polynomial of each of the following numbers over $\mathbb{Q}$.

1. $1 + 2i$
2. $1 + \sqrt{2}$
3. $1 + \sqrt{2i}$
4. $\sqrt{2 + \sqrt[3]{3}}$
5. $\sqrt{3} + \sqrt{5}$
6. $\sqrt{1+\sqrt{2}}$

By minimum polynomial, I think it means polynomials that are monic irreducible. I think the respective answers are:

1. $x^2-2x+5$
2. $x^2-2x- 1$
3. $(x-1)^4+4$
4. $(x^2-2)^3-3$
5. $\displaystyle(x^2-8)^2-60$
6. $(x^2-1)^2-2$

Correct?

[Corrections]

3. $x^2-4x+5$