What is the negative square root of \( \frac{1}{64} \) ? Write your answer as a proper fraction, improper fraction, or whole number.

The negative square root of \( \frac{1}{64} \) is \( -\frac{1}{8} \). This is because the square root of \( \frac{1}{64} \) is \( \frac{1}{8} \), and considering the negative square root, we get \( -\frac{1}{8} \). Speaking of roots, did you know that square roots have been studied for thousands of years? The ancient Babylonians had methods to approximate roots, and even used a form of the square root algorithm, which paved the way for modern mathematics! Math truly has deep historical roots, just like the roots we calculate! In real-world applications, understanding square roots is vital in fields like engineering, finance, and physics. For instance, when calculating the dimensions of a space or the area of land, finding the roots can help you make sure everything fits just right. Knowing how to manipulate fractions, especially with roots, can save you time and effort in practical situations!