Find the product and simplify. Assume the variable \( x \) represents a nonnegative real number. \[ \sqrt{x}(\sqrt{5 x}+5) \]

To simplify the expression \( \sqrt{x}(\sqrt{5 x}+5) \), we start by distributing \( \sqrt{x} \) to both terms inside the parentheses. 1. Distributing \( \sqrt{x} \): \[ \sqrt{x}(\sqrt{5 x}) + \sqrt{x}(5) \] 2. Simplifying each term: - The first term \( \sqrt{x} \cdot \sqrt{5x} \) can be simplified using the property of square roots: \[ \sqrt{x} \cdot \sqrt{5x} = \sqrt{5x^2} = \sqrt{5} \cdot x \] - The second term \( \sqrt{x} \cdot 5 \) is simply: \[ 5\sqrt{x} \] 3. Now combine both simplified terms: \[ \sqrt{5} \cdot x + 5\sqrt{x} \] Therefore, the simplified product is: \[ \sqrt{5} x + 5 \sqrt{x} \]