(160 - 140) / (√40 * √(35/12)) CALCULATE THIS STEP BY STEP

asked by guest
on Nov 24, 2024 at 1:54 am



You asked:

Evaluate the expression: \(\frac{160 - 140}{\sqrt{40} \cdot \sqrt{\frac{35}{12}}}\)

MathBot Answer:

\[\frac{160 - 140}{\sqrt{40} \cdot \sqrt{\frac{35}{12}}} = \frac{2 \sqrt{42}}{7} \approx 1.851640199545102923133133553168\]

\[\begin{aligned}\frac{160 - 140}{\sqrt{40} \cdot \sqrt{\frac{35}{12}}}& = \left(160 - 140\right) \cdot \frac{1}{\sqrt{40} \cdot \sqrt{\frac{35}{12}}}\\& = 20 \cdot \frac{1}{\sqrt{40} \cdot \sqrt{\frac{35}{12}}}\\& = 20 \cdot \frac{1}{2 \cdot \sqrt{10} \cdot \sqrt{\frac{35}{12}}}\\& = 20 \cdot \frac{1}{2 \cdot \sqrt{10} \cdot \frac{1}{6} \cdot \sqrt{105}}\\& = 20 \cdot \frac{1}{\frac{5}{3} \cdot \sqrt{42}}\\& = \frac{2}{7} \cdot \sqrt{42}\end{aligned}\]

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