Multiply. Write your answer in simplest form. \( \sqrt{10} \cdot \sqrt{5} \)

When you multiply square roots, you can combine them under a single square root. So, \( \sqrt{10} \cdot \sqrt{5} = \sqrt{10 \cdot 5} = \sqrt{50} \). To simplify \( \sqrt{50} \), we can factor it into \( \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2} \). Therefore, your final answer is \( 5\sqrt{2} \). Embrace the beauty of square roots! They often pop up in various fields, from architecture to physics. Understanding how to manipulate them not only helps in solving equations but also in real-world situations, like optimizing areas or calculating distances. Next time you're measuring an irregular space, remember that \( \sqrt{50} \) might just be the key to a neat calculation!