To simplify $\sqrt{50}$, follow these steps:

Step 1: Factor the number under the square root

Find the prime factorization of 50:
$50 = 2 \times 5 \times 5$

Step 2: Identify perfect squares

Since $5 \times 5 = 25$ is a perfect square, rewrite the square root:
$\sqrt{50} = \sqrt{25 \times 2}$

Step 3: Use the square root property

The square root of a product can be split:
$\sqrt{50} = \sqrt{25} \times \sqrt{2}$

Since $\sqrt{25} = 5$, we get:
$\sqrt{50} = 5\sqrt{2}$

Final Answer:

$\mathbf{5\sqrt{2}}$

Would you like a deeper explanation or have any questions?

Related Questions:

1. How do you simplify $\sqrt{72}$?
2. What are the rules for simplifying square roots?
3. How do you rationalize the denominator in expressions like $\frac{1}{\sqrt{5}}$?
4. What is the square root of 200 simplified?
5. How do you estimate the value of $\sqrt{50}$ without a calculator?

Tip:

To simplify square roots, always look for the largest perfect square factor! 🚀