Put $(7+5\sqrt{2})^{\frac{1}{3}}$ in the form $x+y(\sqrt{2})$ I said, let:
$(7+5\sqrt{2})^{\frac{1}{3}}=((x+y\sqrt{2})^{3})^{\frac{1}{3}}$
Therefore, 
$(7+5\sqrt{2})=(x+y\sqrt{2})^{3}$
Hence,
$(7+5\sqrt{2})=x^{3}+3x^{2}y(\sqrt{2})+3xy^{2}(\sqrt{2})^{2}+y^{3}
(\sqrt{2})^3$
However, from here how do I go? Anyone have any ideas?
Thanks a bunch in advance.

Hint:
Notice
\begin{align}
7+5\sqrt{2}&=2\sqrt{2}+3(2)(1)+3(\sqrt{2})(1)+1\\
&=(\sqrt{2})^3+3(\sqrt{2})^2(1)+3(\sqrt{2})(1)^2+(1)^3
\end{align}
Can you recognize this pattern?
