Select the correct answer. Which expression is equivalent to \( 10 \sqrt{5} \) ? \[ \begin{array}{l}\text { A. } \sqrt{500} \\ \text { B. } \sqrt{105} \\ \text { C. } \sqrt{50} \\ \text { D. } \sqrt{15}\end{array} \]

To find which expression is equivalent to \( 10 \sqrt{5} \), we can square it to simplify, giving us \( (10 \sqrt{5})^2 = 100 \cdot 5 = 500 \). Now we need to see which option also simplifies to 500 when squared. A. \( \sqrt{500} \) simplifies to \( \sqrt{100 \cdot 5} = 10 \sqrt{5} \), which is exactly what we started with. Thus, the correct answer is **A.** For an interesting twist: did you know that the square root of a number can sometimes seem elusive? It’s like a magician’s trick! The classic \(\sqrt{500}\) gives you a number that releases the magic of 10 and 5, showing us how algebra can either mystify or clarify—depending on how we approach it. Feel free to explore the concept of rationalizing the denominator; it’s like rounding up the variables and making them cooperate! For instance, if you ever find a messy fraction with a square root in the denominator, remember to multiply both top and bottom by that square root to simplify your expression. Just like tidying up a room, having everything neat and organized makes it easier to get the answers you need!