Solving an cquation of the form \( x^{2}= \) a using the square root proper Solve \( v^{2}=25 \), where \( v \) is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". \( \qquad v=\square] \)

To solve the equation \( v^{2} = 25 \) using the square root method, we take the square root of both sides. Remember, when you take the square root of a squared variable, you must consider both the positive and negative roots. Therefore, we have: \( v = \pm \sqrt{25} \) This leads to: \( v = \pm 5 \) So the complete solution set is: \( v = 5, -5 \) --- Did you know that the concept of solving equations through squaring and square roots dates back to ancient civilizations, like the Babylonians around 2000 BC? They had a knack for solving quadratic equations, even before symbolic algebra was a thing! It's fascinating how this foundational knowledge has shaped mathematics as we know it today. One common mistake when solving equations like this is forgetting to include both the positive and negative solutions after taking the square root. Always remember that squaring a number eliminates its sign, so you have to consider both possibilities to ensure you find all potential solutions.