\( -3 \sqrt{8 x^{3}} \) and \( x^{2} \sqrt{18 x} \)

Let's simplify each of the given expressions step-by-step. ### 1. Simplifying \( -3 \sqrt{8x^{3}} \) **Step 1:** Factor the expression inside the square root. \[ \sqrt{8x^3} = \sqrt{4 \times 2 \times x^2 \times x} = \sqrt{4x^2} \times \sqrt{2x} \] **Step 2:** Simplify the square roots. \[ \sqrt{4x^2} = 2x \quad \text{and} \quad \sqrt{2x} \text{ remains as is} \] **Step 3:** Combine the simplified terms. \[ \sqrt{8x^3} = 2x \sqrt{2x} \] **Step 4:** Multiply by the coefficient outside the square root. \[ -3 \sqrt{8x^3} = -3 \times 2x \sqrt{2x} = -6x \sqrt{2x} \] **Final Simplified Form:** \[ -6x \sqrt{2x} \] --- ### 2. Simplifying \( x^{2} \sqrt{18x} \) **Step 1:** Factor the expression inside the square root. \[ \sqrt{18x} = \sqrt{9 \times 2 \times x} = \sqrt{9} \times \sqrt{2x} \] **Step 2:** Simplify the square roots. \[ \sqrt{9} = 3 \quad \text{and} \quad \sqrt{2x} \text{ remains as is} \] **Step 3:** Combine the simplified terms. \[ \sqrt{18x} = 3 \sqrt{2x} \] **Step 4:** Multiply by the coefficient outside the square root. \[ x^2 \sqrt{18x} = x^2 \times 3 \sqrt{2x} = 3x^2 \sqrt{2x} \] **Final Simplified Form:** \[ 3x^2 \sqrt{2x} \] --- ### **Summary of Simplified Expressions:** 1. \( -3 \sqrt{8x^{3}} = -6x \sqrt{2x} \) 2. \( x^{2} \sqrt{18x} = 3x^2 \sqrt{2x} \)