Question
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Answer
a) \(\sqrt{\frac{3}{5}} = \frac{\sqrt{15}}{5} \approx 0{,}7746\)
Solution
a) \(\sqrt{\frac{3}{5}} = \frac{\sqrt{15}}{5} \approx 0{,}7746\)
**Erläuterung:**
1. **Rationalisierung des Nenners:**
\[
\sqrt{\frac{3}{5}} = \frac{\sqrt{3}}{\sqrt{5}} = \frac{\sqrt{3} \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}} = \frac{\sqrt{15}}{5}
\]
2. **Dezimaldarstellung:**
\[
\frac{\sqrt{15}}{5} \approx \frac{3{,}872983346}{5} \approx 0{,}7746
\]
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Simplify this solution Beyond the Answer
The value of \( \sqrt{\frac{3}{5}} \) can be simplified by expressing it as \( \frac{\sqrt{3}}{\sqrt{5}} \). This gives us an approximate numerical value of about 0.7746 when calculated. It’s a neat example of using square roots with fractions! In daily life, this expression can pop up in various fields like architecture, physics, and engineering when dealing with proportions. Understanding how to manipulate square roots aids in problem-solving, whether you're calculating diagonal lengths or optimizing material usage!
