Pierādīt, ka \(\sqrt{17-12 \sqrt{2}}+\sqrt{3-2 \sqrt{2}}+\sqrt{3+2 \sqrt{2}}=3\).
Katru zemsaknes izteiksmi izteiksim kā summas vai starpības kvadrātu un veiksim ekvivalentus pārveidojumus:
\[\begin{gathered} \sqrt{17-12 \sqrt{2}}+\sqrt{3-2 \sqrt{2}}+\sqrt{3+2 \sqrt{2}}= \\ =\sqrt{3^{2}-2 \cdot 3 \cdot 2 \sqrt{2}+(2 \sqrt{2})^{2}}+\sqrt{(\sqrt{2})^{2}-2 \cdot \sqrt{2} \cdot 1+1^{2}}+\sqrt{(\sqrt{2})^{2}+2 \cdot \sqrt{2} \cdot 1+1^{2}}= \\ =\sqrt{(3-2 \sqrt{2})^{2}}+\sqrt{(\sqrt{2}-1)^{2}}+\sqrt{(\sqrt{2}+1)^{2}}=|3-2 \sqrt{2}|+|\sqrt{2}-1|+|\sqrt{2}+1|= \\ =3-2 \sqrt{2}+\sqrt{2}-1+\sqrt{2}+1=3 . \end{gathered}\]