How do you simplify √50?

To simplify √50, express it as 5√2 by factoring out the square root of the largest perfect square.

To break this down, start by identifying the factors of 50. The number 50 can be factored into 25 and 2, where 25 is a perfect square (since 25 = 5²). This allows us to rewrite √50 as √(25 × 2). Using the property of square roots that √(a × b) = √a × √b, we can separate this into √25 × √2. Since the square root of 25 is 5, this simplifies to 5√2. Therefore, √50 simplifies to 5√2.

This method works because it leverages the property of square roots and the fact that 25 is a perfect square, making the simplification straightforward. This approach is useful for simplifying square roots of numbers that are not perfect squares by breaking them down into factors that include a perfect square.