1. **State the problem:** Calculate $\sqrt{2}^3$. 2. **Recall the properties of exponents:** For any positive number $a$ and rational exponent $m/n$, $a^{m/n} = (\sqrt[n]{a})^m$. 3. **Rewrite the expression:** $\sqrt{2} = 2^{1/2}$, so $\sqrt{2}^3 = (2^{1/2})^3$. 4. **Apply the power of a power rule:** $(a^m)^n = a^{m \times n}$, so $(2^{1/2})^3 = 2^{(1/2) \times 3} = 2^{3/2}$. 5. **Simplify the exponent:** $2^{3/2} = 2^{1 + 1/2} = 2^1 \times 2^{1/2} = 2 \times \sqrt{2}$. 6. **Final answer:** $\sqrt{2}^3 = 2 \sqrt{2}$.