Identify the most simplified version of the expression below: \[ \begin{array}{ll}\frac{5 \sqrt{8}}{\sqrt{2}} \\ \text { A) } 20 & \text { C) } \frac{5 \sqrt{2}}{2} \\ \text { B) } 10 & \text { D) } 5 \sqrt{2}\end{array} \]
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To simplify the expression \(\frac{5 \sqrt{8}}{\sqrt{2}}\), we start by simplifying \(\sqrt{8}\). We know that: \[ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \] Now substituting this back into our expression gives: \[ \frac{5 \sqrt{8}}{\sqrt{2}} = \frac{5 (2 \sqrt{2})}{\sqrt{2}} = \frac{10 \sqrt{2}}{\sqrt{2}} \] The \(\sqrt{2}\) in the numerator and denominator cancels out, leading us to: \[ 10 \] Thus, the most simplified version of the expression is \(10\), which corresponds to option B.