Pregunta
Identify the most simplified version of the expression below: \[ \begin{array}{ll}\frac{5 \sqrt{8}}{\sqrt{2}} \\ \text { A) } 20 & \text { C) } \frac{5 \sqrt{2}}{2} \\ \text { B) } 10 & \text { D) } 5 \sqrt{2}\end{array} \]
Ask by Moran Cross. in the United States
Feb 27,2025
Solución de inteligencia artificial de Upstudy
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The most simplified version of the expression is 10 (option B).
Solución
We begin with the expression (5√8) / √2. Notice that √8 can be simplified because √8 = 2√2. So, replacing √8 gives:
(5 * 2√2) / √2 = (10√2) / √2
Now, the √2 in the numerator cancels with the √2 in the denominator:
(10√2) / √2 = 10
Thus, the most simplified version of the expression is 10 (option B).
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Como
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Extra Insights
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.
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