Setect ine coinect aniswer. \[ \begin{array}{l}\text { Simplify, } \\ \sqrt{75}\end{array} \] A. \( 32 \sqrt{5} \) B. \( 15 \sqrt{5} \) C. \( 25 \sqrt{3} \) D. \( 5 \sqrt{3} \)

To simplify \(\sqrt{75}\), we can start by factoring 75 into its prime components: \(75 = 25 \times 3\). We know that 25 is a perfect square, equal to \(5^2\). Therefore, we can express the square root as: \[ \sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \cdot \sqrt{3} = 5\sqrt{3}. \] Thus, the correct answer is D. \(5 \sqrt{3}\). Now, speaking of square roots, did you know that the concept of square roots dates back to ancient civilizations? The Babylonians had an approximate method for calculating the square root as early as 2000 BC! They even used them to solve problems related to land measurement. Additionally, for those interested in tackling square root problems, remember always to look for perfect squares within the number you’re simplifying. Common mistakes include not fully factoring the number or mistaking the square root of a product for the product of the square roots! Keep this in mind, and you'll be breezing through problems in no time!