Question

question
go step by step to reduce the radical.
\\(\sqrt{208}\\)
\\(\sqrt{\square}\\ \sqrt{\square}\\)

Explanation:

Step1: Factor out perfect square

Find the largest perfect square factor of 208. $208 = 16 \times 13$, where 16 is a perfect square.
$\sqrt{208} = \sqrt{16 \times 13}$

Step2: Split radical using product rule

Apply $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$
$\sqrt{16 \times 13} = \sqrt{16} \times \sqrt{13}$

Step3: Simplify perfect square radical

Calculate $\sqrt{16} = 4$
$\sqrt{16} \times \sqrt{13} = 4\sqrt{13}$

Answer:

The filled blanks are $\boldsymbol{\sqrt{16}}$ and $\boldsymbol{\sqrt{13}}$, and the simplified radical is $\boldsymbol{4\sqrt{13}}$