Simplify: $\sqrt{17+12\sqrt{2}}$.

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1. We want to simplify $\sqrt{17+12\sqrt{2}}$.
2. Write it as $a+b\sqrt{2}$ with integers $a,b$.
3. Square both sides: $(a+b\sqrt{2})^2=a^2+2b^2+2ab\sqrt{2}=17+12\sqrt{2}$.
4. Match parts: $a^2+2b^2=17$ and $2ab=12$, so $ab=6$. Try $a=3,b=2$ because $3\cdot2=6$ and $9+8=17$.
5. So $\sqrt{17+12\sqrt{2}}=3+2\sqrt{2}$.
FINAL_ANSWER: c

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