Simplify the following radical expression. \( \sqrt[3]{40} \)

To simplify the radical expression \( \sqrt[3]{40} \), follow these steps: 1. **Factor the Radicand:** Start by factoring the number inside the cube root (the radicand) into its prime factors. \[ 40 = 8 \times 5 \] Here, \( 8 \) is a perfect cube because \( 8 = 2^3 \). 2. **Rewrite the Cube Root Using the Factors:** Use the property of radicals that allows you to separate the cube root of a product into the product of cube roots. \[ \sqrt[3]{40} = \sqrt[3]{8 \times 5} = \sqrt[3]{8} \times \sqrt[3]{5} \] 3. **Simplify the Cube Root of the Perfect Cube:** Since \( \sqrt[3]{8} = 2 \), substitute this value back into the expression. \[ \sqrt[3]{8} \times \sqrt[3]{5} = 2 \times \sqrt[3]{5} \] 4. **Final Simplified Form:** Combine the terms to write the simplified expression. \[ \sqrt[3]{40} = 2 \sqrt[3]{5} \] **Answer:** \[ \sqrt[3]{40} = 2\, \sqrt[3]{5} \]