To simplify $\sqrt{50}$, we need to break 50 into its prime factors and extract any perfect squares from under the square root.

1. Start by factoring 50: $50 = 25 \times 2$ Notice that 25 is a perfect square because $\sqrt{25} = 5$.

2. Now, we can split the square root: $\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2}$

3. Simplifying further: $\sqrt{50} = 5 \times \sqrt{2}$

So, the simplified form of $\sqrt{50}$ is: $\boxed{5\sqrt{2}}$

Would you like any additional details or clarifications?

Related Questions:

1. How would you simplify $\sqrt{72}$?
2. What are the steps to simplify $\sqrt{98}$?
3. How do you determine if a number is a perfect square?
4. What is the process for simplifying cube roots?
5. How do you simplify $\sqrt{32}$?

Tip:

Always break down the number under the square root into its prime factors to check for perfect squares that can be simplified.