4) \( \sqrt{6} \times 2 \sqrt{3} \)

To simplify the expression \( \sqrt{6} \times 2 \sqrt{3} \), follow these steps: 1. **Rearrange the Terms:** You can rearrange the constants and the square roots to make the multiplication clearer: \[ \sqrt{6} \times 2 \sqrt{3} = 2 \times \sqrt{6} \times \sqrt{3} \] 2. **Multiply the Square Roots:** Use the property of square roots that \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\): \[ \sqrt{6} \times \sqrt{3} = \sqrt{6 \times 3} = \sqrt{18} \] 3. **Simplify \(\sqrt{18}\):** Factor 18 into a product of a perfect square and another factor: \[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \] 4. **Combine All Parts:** Multiply the constant outside the square root by the simplified square root: \[ 2 \times 3\sqrt{2} = 6\sqrt{2} \] **Final Answer:** \[ \sqrt{6} \times 2 \sqrt{3} = 6\sqrt{2} \]