1. **State the problem:** Simplify the surd $\sqrt[3]{56}$ completely. 2. **Recall the formula and rules:** To simplify cube roots, factor the number inside the root into prime factors and look for cubes. 3. **Factorize 56:** $$56 = 2 \times 2 \times 2 \times 7 = 2^3 \times 7$$ 4. **Apply cube root to the factorization:** $$\sqrt[3]{56} = \sqrt[3]{2^3 \times 7}$$ 5. **Use the property:** $$\sqrt[3]{a \times b} = \sqrt[3]{a} \times \sqrt[3]{b}$$ 6. **Simplify the cube root of $2^3$:** $$\sqrt[3]{2^3} = 2$$ 7. **Rewrite the expression:** $$\sqrt[3]{56} = 2 \times \sqrt[3]{7} = 2\sqrt[3]{7}$$ 8. **Check the options:** None of the options match $2\sqrt[3]{7}$, so the answer is E: None of these. **Final answer:** $2\sqrt[3]{7}$