Obliczamy wartość danego wyrażenia.

${\left(\sqrt{3-2\sqrt{2}}\right)}^3={\left(\sqrt{3-2\sqrt{2}}\right)}^2\cdot \sqrt{3-2\sqrt{2}}=\left(3-2\sqrt{2}\right)\cdot \sqrt{3-2\sqrt{2}}=\left(3-2\sqrt{2}\right)\cdot \sqrt{2-2\sqrt{2}+1}=\left(3-2\sqrt{2}\right)\cdot \sqrt{{\left(\sqrt{2}\right)}^2-2\cdot \sqrt{2}\cdot 2+1^2}=\left(3-2\sqrt{2}\right)\cdot \sqrt{{\left(\sqrt{2}-1\right)}^2}=\left(3-2\sqrt{2}\right)\cdot \left|\sqrt{2}-1\right|=\left(3-2\sqrt{2}\right)\cdot \left(\sqrt{2}-1\right)=3\sqrt{2}-3-4+2\sqrt{2}=5\sqrt{2}-7$  

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Prawidłowa odpowiedź to B.