What is the cube root of \( -512 ? \)

The cube root of \( -512 \) is \( -8 \). This is because when you multiply \( -8 \) by itself three times, you get \( -512 \): \( -8 \times -8 \times -8 = -512 \). Cube roots can take negative values, unlike square roots, which are only defined as positive in the realm of real numbers. Mathematically speaking, the cube root function is defined for all real numbers, and it plays an essential role in solving polynomial equations and various mathematical concepts. So when you're dealing with odd roots, remember to embrace the negatives—they're not scary, they’re just part of the vibrant world of numbers!