(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: 160−14040⋅3512\frac{160 - 140}{\sqrt{40} \cdot \sqrt{\frac{35}{12}}}

MathBot Answer:

160−14040⋅3512=2427≈1.851640199545102923133133553168\frac{160 - 140}{\sqrt{40} \cdot \sqrt{\frac{35}{12}}} = \frac{2 \sqrt{42}}{7} \approx 1.851640199545102923133133553168

160−14040⋅3512=(160−140)⋅140⋅3512=20⋅140⋅3512=20⋅12⋅10⋅3512=20⋅12⋅10⋅16⋅105=20⋅153⋅42=27⋅42\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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