Simplify \( \sqrt{50} \)

To simplify \( \sqrt{50} \), you can break it down into its prime factors: \( 50 = 25 \times 2 \) or \( 50 = 5^2 \times 2 \). Using the property of square roots, we can separate it as follows: \[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}. \] So, \( \sqrt{50} \) simplifies to \( 5\sqrt{2} \). Remember, when simplifying square roots, always look for perfect squares to make things easier! It's like transforming a complicated puzzle into an easier one by recognizing those familiar shapes.