The problem asks to reduce the radical $\sqrt{208}$ step by step.

1. Problem Description

The problem asks to reduce the radical $\sqrt{208}$ step by step.

2. Solution Steps

To reduce the radical $\sqrt{208}$, we first find the prime factorization of

2

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8. $208 = 2 \times 104 = 2 \times 2 \times 52 = 2 \times 2 \times 2 \times 26 = 2 \times 2 \times 2 \times 2 \times 13 = 2^4 \times 13$.

Therefore, we have

$\sqrt{208} = \sqrt{2^4 \times 13} = \sqrt{2^4} \times \sqrt{13} = 2^2 \sqrt{13} = 4\sqrt{13}$.

So the steps are:

$\sqrt{208} = \sqrt{16 \times 13} = \sqrt{16} \times \sqrt{13} = 4\sqrt{13}$.

3. Final Answer

$\sqrt{208} = \sqrt{16} \cdot \sqrt{13} = 4\sqrt{13}$.

First box: $16$

Second box: $13$

Third box: $4$