Paul Beguelin

It's also important to note that every positive number has two square roots: one positive and one negative. So, while we primarily focus on the principal (positive) square root, √27 = 3√3, it is equally true that -3√3 is also a square root of 27, because (-3√3) × (-3√3) = 9 × 3 = 27. This concept is fundamental in algebra, especially when solving quadratic equations like x² = 27. The solutions would be x = √27 and x = -√27, or x = 3√3 and x = -3√3. Forgetting the negative root is a common mistake, so always remember that the radical symbol (√) itself denotes only the principal (non-negative) square root, but the equation x² = a has two solutions.