Solve the following equation by using the square root property. Write all radicals in simplest form. \( 3 x^{2}-24=0 \)

To solve the equation \( 3x^{2} - 24 = 0 \) using the square root property, first isolate the \( x^{2} \) term. Add 24 to both sides to get \( 3x^{2} = 24 \). Then, divide both sides by 3, yielding \( x^{2} = 8 \). Now, take the square root of both sides: \( x = \pm \sqrt{8} \). Simplifying \( \sqrt{8} \) gives \( \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2} \). Therefore, the solutions are \( x = 2\sqrt{2} \) and \( x = -2\sqrt{2} \). Radicals can often seem daunting, but they show up more in everyday life than you might think! From architecture (think of those beautiful triangular roof designs!) to nature (the way trees branch out can be described using radical functions), understanding the principles of radicals helps us appreciate the underlying patterns all around us. If you're ever confused by radical expressions, remember that simplifying is key! A common mistake is forgetting to simplify the radical fully or misplacing negative signs. Always double-check your work: ensuring you've handled signs correctly and simplifying any radicals to their simplest form can save you headaches later on. Plus, when you write things clearly, it makes it easier for others to understand your thought process!