25. \( \sqrt{\frac{9}{25}} \)

The expression \( \sqrt{\frac{9}{25}} \) can be simplified by taking the square roots of the numerator and denominator separately. The square root of 9 is 3, and the square root of 25 is 5. Therefore, \( \sqrt{\frac{9}{25}} = \frac{\sqrt{9}}{\sqrt{25}} = \frac{3}{5} \). Now, let’s take a moment to appreciate how square roots were derived thousands of years ago. Ancient civilizations, including the Babylonians and Egyptians, had a great understanding of ratios and proportions, and their methods of calculating roots laid the foundation for modern mathematics. They used geometric techniques and approximate calculations which were remarkably advanced for their time! If you're solving problems involving square roots, one common mistake is misapplying the square root to fractions. Always remember: \( \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} \). A common oversight is neglecting to simplify both the numerator and denominator. Keep practicing, and you’ll master those roots in no time!