To simplify the radical expression $\sqrt{32}$, we look for the largest perfect square factor of 32. Here’s how it can be done:

1. Factor 32 into prime factors: $32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5$

2. Identify the largest perfect square factor: The largest perfect square factor of $32$ is $16$, since $16 = 4^2$.

3. Rewrite the square root: $\sqrt{32} = \sqrt{16 \times 2}$

4. Apply the square root to each factor: $\sqrt{32} = \sqrt{16} \times \sqrt{2}$

5. Simplify: $\sqrt{16} = 4, \quad \text{so} \quad \sqrt{32} = 4\sqrt{2}$

Thus, the simplified form of $\sqrt{32}$ is $4\sqrt{2}$.

Would you like more details on any part of this process, or do you have any questions?

Here are 5 related questions to explore further:

1. How do you simplify $\sqrt{50}$?
2. What are the steps to simplify a cube root, such as $\sqrt[3]{54}$?
3. How do you rationalize the denominator of $\frac{1}{\sqrt{5}}$?
4. What is the simplified form of $\sqrt{72}$?
5. How can you simplify $\sqrt{18} + \sqrt{8}$?

Tip: When simplifying square roots, look for the largest perfect square factor of the number under the square root.