Add. Assume that all variables represent positive real numbers. \( 6 \sqrt{2 x^{3}}+3 x \sqrt{18 x} \) \( 6 \sqrt{2 x^{3}}+3 x \sqrt{18 x}=\square \) (Type an exact answer, using rasicals as needed. Simplify your answer.)

To simplify \( 6 \sqrt{2 x^{3}} + 3 x \sqrt{18 x} \), let’s first simplify \( \sqrt{18 x} \). \[\sqrt{18 x} = \sqrt{9 \cdot 2 \cdot x} = \sqrt{9} \cdot \sqrt{2} \cdot \sqrt{x} = 3 \sqrt{2} \sqrt{x} = 3 \sqrt{2 x}.\] Now, substituting this back into the equation gives us: \[ 6 \sqrt{2 x^{3}} + 3 x \cdot 3 \sqrt{2 x}.\] This can be rewritten as: \[ 6 \sqrt{2 x^{3}} + 9 x \sqrt{2 x}.\] Next, we can express \( \sqrt{2 x^3} \) as: \[\sqrt{2 x^3} = \sqrt{2} \cdot \sqrt{x^3} = \sqrt{2} \cdot x \cdot \sqrt{x} = x \sqrt{2 x}.\] Now we can substitute this back into the expression: \[ 6(x \sqrt{2 x}) + 9(x \sqrt{2 x}) = (6 + 9)(x \sqrt{2 x}) = 15(x \sqrt{2 x}). \] Thus, the simplified expression is: \[ 15 x \sqrt{2 x}. \] So, \[ 6 \sqrt{2 x^{3}} + 3 x \sqrt{18 x} = 15 x \sqrt{2 x}. \]