Let's go through the process of simplifying each radical step by step.

1. Simplifying $\sqrt{16}$

Step 1: Identify if the number inside the square root is a perfect square.

• $16$ is a perfect square because it can be written as $4 \times 4$.

Step 2: Take the square root of the perfect square.

$\sqrt{16} = 4$

Conclusion: The simplified form of $\sqrt{16}$ is $4$.

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2. Simplifying $\sqrt{32}$

Step 1: Factor the number inside the square root into its prime factors or into a product that includes a perfect square.

• $32$ can be factored as $32 = 16 \times 2$.

Step 2: Break down the square root into the square root of each factor.

$\sqrt{32} = \sqrt{16 \times 2}$

Step 3: Simplify the square root of the perfect square.

• Since $\sqrt{16} = 4$, substitute this into the equation:

$\sqrt{32} = 4 \times \sqrt{2}$

Conclusion: The simplified form of $\sqrt{32}$ is $4\sqrt{2}$.

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These steps can be applied to any square root simplification process.

Would you like any further details or explanations on this? Here are 5 additional related questions:

1. How do you simplify $\sqrt{50}$ step by step?
2. What steps would you take to simplify $\sqrt{72}$?
3. Can you show the steps for simplifying $\sqrt{45}$?
4. What is the step-by-step process for simplifying $\sqrt{18}$?
5. How do you simplify a square root that is not a perfect square?

Tip: When simplifying radicals, always check if the number inside the radical has a perfect square factor, as this will make the simplification easier.