5√32/∛8 ÷(√50)/(√32)

asked by guest
on Nov 12, 2024 at 5:03 pm



You asked:

Evaluate the expression: 532835032\frac{\frac{\frac{5 \sqrt{32}}{\sqrt[3]{8}}}{\sqrt{50}}}{\sqrt{32}}

MathBot Answer:

532835032=24≈0.35355339059327376220042218105242\frac{\frac{\frac{5 \sqrt{32}}{\sqrt[3]{8}}}{\sqrt{50}}}{\sqrt{32}} = \frac{\sqrt{2}}{4} \approx 0.35355339059327376220042218105242

532835032=5⋅32⋅183⋅150⋅132=5⋅4⋅2⋅183⋅150⋅132=5⋅4⋅2⋅12⋅150⋅132=5⋅4⋅2⋅12⋅15⋅2⋅132=5⋅4⋅2⋅12⋅110⋅2⋅132=5⋅4⋅2⋅12⋅110⋅2⋅14⋅2=5⋅4⋅2⋅12⋅140=20⋅2⋅12⋅140=10⋅2⋅140=14⋅2\begin{aligned}\frac{\frac{\frac{5 \sqrt{32}}{\sqrt[3]{8}}}{\sqrt{50}}}{\sqrt{32}}&=5 \cdot \sqrt{32} \cdot \frac{1}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt{50}} \cdot \frac{1}{\sqrt{32}}\\&=5 \cdot 4 \cdot \sqrt{2} \cdot \frac{1}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt{50}} \cdot \frac{1}{\sqrt{32}}\\&=5 \cdot 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \frac{1}{\sqrt{50}} \cdot \frac{1}{\sqrt{32}}\\&=5 \cdot 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \frac{1}{5 \cdot \sqrt{2}} \cdot \frac{1}{\sqrt{32}}\\&=5 \cdot 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \frac{1}{10} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{32}}\\&=5 \cdot 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \frac{1}{10} \cdot \sqrt{2} \cdot \frac{1}{4 \cdot \sqrt{2}}\\&=5 \cdot 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \frac{1}{40}\\&=20 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \frac{1}{40}\\&=10 \cdot \sqrt{2} \cdot \frac{1}{40}\\&=\frac{1}{4} \cdot \sqrt{2}\end{aligned}

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