5√32/∛8 ÷(√50)/(√32)

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



You asked:

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

MathBot Answer:

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

\[\begin{aligned}\frac{\frac{\frac{5 \cdot \sqrt{32}}{\sqrt[3]{8}}}{\sqrt{50}}}{\sqrt{32}}& = 5 \cdot \sqrt{32} \cdot \frac{1}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt{50}} \cdot \frac{1}{\sqrt{32}}\\& = 5 \cdot 4 \cdot \sqrt{2} \cdot \frac{1}{\sqrt[3]{8}} \cdot \frac{1}{\sqrt{50}} \cdot \frac{1}{\sqrt{32}}\\& = 5 \cdot 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \frac{1}{\sqrt{50}} \cdot \frac{1}{\sqrt{32}}\\& = 5 \cdot 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \frac{1}{5 \cdot \sqrt{2}} \cdot \frac{1}{\sqrt{32}}\\& = 5 \cdot 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \frac{1}{10} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{32}}\\& = 5 \cdot 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \frac{1}{10} \cdot \sqrt{2} \cdot \frac{1}{4 \cdot \sqrt{2}}\\& = 5 \cdot 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \frac{1}{40}\\& = 20 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \frac{1}{40}\\& = 10 \cdot \sqrt{2} \cdot \frac{1}{40}\\& = \frac{1}{4} \cdot \sqrt{2}\end{aligned}\]

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