2(√3/6 (+√2)/√2)^(−1)+3(√2/4 (+√3)/√3)^(−1)

asked by guest
on Oct 23, 2024 at 4:33 am



You asked:

Evaluate the expression: \(2 \cdot {\left( \frac{\frac{\sqrt{3}}{6 \cdot \sqrt{2}}}{\sqrt{2}} \right)}^{-1} + 3 \cdot {\left( \frac{\frac{\sqrt{2}}{4 \cdot \sqrt{3}}}{\sqrt{3}} \right)}^{-1}\)

MathBot Answer:

\[2 \cdot {\left( \frac{\frac{\sqrt{3}}{6 \cdot \sqrt{2}}}{\sqrt{2}} \right)}^{-1} + 3 \cdot {\left( \frac{\frac{\sqrt{2}}{4 \cdot \sqrt{3}}}{\sqrt{3}} \right)}^{-1} = 8 \sqrt{3} + 18 \sqrt{2} \approx 39.31225058326672922664996776782154\]

\[\begin{aligned}2 \cdot {\left( \frac{\frac{\sqrt{3}}{6 \cdot \sqrt{2}}}{\sqrt{2}} \right)}^{-1} + 3 \cdot {\left( \frac{\frac{\sqrt{2}}{4 \cdot \sqrt{3}}}{\sqrt{3}} \right)}^{-1}& = 2 \cdot \frac{1}{\sqrt{3} \cdot \frac{1}{6 \cdot \sqrt{2}} \cdot \frac{1}{\sqrt{2}}} + 3 \cdot \frac{1}{\sqrt{2} \cdot \frac{1}{4 \cdot \sqrt{3}} \cdot \frac{1}{\sqrt{3}}}\\& = 2 \cdot \frac{1}{\sqrt{3} \cdot \frac{1}{12} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{2}}} + 3 \cdot \frac{1}{\sqrt{2} \cdot \frac{1}{4 \cdot \sqrt{3}} \cdot \frac{1}{\sqrt{3}}}\\& = 2 \cdot \frac{1}{\sqrt{3} \cdot \frac{1}{12}} + 3 \cdot \frac{1}{\sqrt{2} \cdot \frac{1}{4 \cdot \sqrt{3}} \cdot \frac{1}{\sqrt{3}}}\\& = 2 \cdot \frac{1}{\frac{1}{12} \cdot \sqrt{3}} + 3 \cdot \frac{1}{\sqrt{2} \cdot \frac{1}{4 \cdot \sqrt{3}} \cdot \frac{1}{\sqrt{3}}}\\& = 8 \cdot \sqrt{3} + 3 \cdot \frac{1}{\sqrt{2} \cdot \frac{1}{4 \cdot \sqrt{3}} \cdot \frac{1}{\sqrt{3}}}\\& = 8 \cdot \sqrt{3} + 3 \cdot \frac{1}{\sqrt{2} \cdot \frac{1}{12} \cdot \sqrt{3} \cdot \frac{1}{\sqrt{3}}}\\& = 8 \cdot \sqrt{3} + 3 \cdot \frac{1}{\sqrt{2} \cdot \frac{1}{12}}\\& = 8 \cdot \sqrt{3} + 3 \cdot \frac{1}{\frac{1}{12} \cdot \sqrt{2}}\\& = 8 \cdot \sqrt{3} + 18 \cdot \sqrt{2}\end{aligned}\]

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