Multiply the radical expression. Express numbers in simplified form using integers, fractions, or radicals.

Sure, I'd be happy to help you multiply radical expressions! However, I need the specific expressions you'd like to multiply to provide a detailed solution. **In the meantime, here's a general guide on how to multiply radical expressions:** ### **Steps to Multiply Radical Expressions** 1. **Simplify Each Radical (if possible):** - Break down each number inside the radical into its prime factors. - Identify and extract any square factors (for square roots) or appropriate factors for other types of roots. 2. **Multiply the Coefficients:** - Multiply the numerical coefficients (the numbers outside the radicals) directly. 3. **Multiply the Radicands:** - Multiply the numbers inside the radicals together. 4. **Simplify the Resulting Radical:** - After multiplication, simplify the radical by extracting any possible factors. ### **Example 1: Multiplying Square Roots** **Problem:** Multiply √2 × √8 **Solution:** 1. **Multiply the radicands:** \[ \sqrt{2} \times \sqrt{8} = \sqrt{2 \times 8} = \sqrt{16} \] 2. **Simplify the radical:** \[ \sqrt{16} = 4 \] **Answer:** 4 ### **Example 2: Multiplying with Coefficients** **Problem:** Multiply 3√5 × 2√20 **Solution:** 1. **Multiply the coefficients:** \[ 3 \times 2 = 6 \] 2. **Multiply the radicands:** \[ \sqrt{5} \times \sqrt{20} = \sqrt{5 \times 20} = \sqrt{100} \] 3. **Simplify the radical:** \[ \sqrt{100} = 10 \] 4. **Combine the results:** \[ 6 \times 10 = 60 \] **Answer:** 60 ### **Example 3: Multiplying Different Types of Radicals** **Problem:** Multiply √3 × ³√27 **Solution:** 1. **Simplify each radical:** \[ \sqrt{3} \text{ is already simplified} \] \[ ³\sqrt{27} = 3 \quad \text{(since } 3^3 = 27) \] 2. **Multiply the results:** \[ \sqrt{3} \times 3 = 3\sqrt{3} \] **Answer:** \( 3\sqrt{3} \) --- Feel free to provide the specific radical expressions you'd like to multiply, and I can walk you through the exact solution!