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 radicals as needed. Simplify your answer.)

To simplify the expression \( 6 \sqrt{2 x^{3}} + 3 x \sqrt{18 x} \), we start by simplifying each term. 1. The first term is \( 6 \sqrt{2 x^{3}} \), which can be rewritten as: \[ 6 \sqrt{2} \sqrt{x^{3}} = 6 \sqrt{2} x^{3/2} \] 2. The second term is \( 3 x \sqrt{18 x} \). First, let's simplify \( \sqrt{18 x} \): \[ \sqrt{18 x} = \sqrt{18} \sqrt{x} = 3 \sqrt{2} \sqrt{x} \] Therefore, we have: \[ 3 x \sqrt{18 x} = 3 x (3 \sqrt{2} \sqrt{x}) = 9 \sqrt{2} x^{3/2} \] Now, we can combine the two simplified terms: \[ 6 \sqrt{2} x^{3/2} + 9 \sqrt{2} x^{3/2} \] Adding these together gives: \[ (6 + 9) \sqrt{2} x^{3/2} = 15 \sqrt{2} x^{3/2} \] Thus, the simplified expression is: \[ 15 \sqrt{2} x^{3/2} = \square \]