2√128−√200 + √24+3√6
You asked:
Evaluate the expression: \(2 \cdot \sqrt{128} - \sqrt{200} + \sqrt{24} + 3 \cdot \sqrt{6}\)
MathBot Answer:
\[2 \cdot \sqrt{128} - \sqrt{200} + \sqrt{24} + 3 \cdot \sqrt{6} = 6 \sqrt{2} + 5 \sqrt{6} \approx 20.73273008815446078379655271878765\]
\[\begin{aligned}2 \cdot \sqrt{128} - \sqrt{200} + \sqrt{24} + 3 \cdot \sqrt{6}& = 2 \cdot 8 \cdot \sqrt{2} - \sqrt{200} + \sqrt{24} + 3 \cdot \sqrt{6}\\& = 16 \cdot \sqrt{2} - \sqrt{200} + \sqrt{24} + 3 \cdot \sqrt{6}\\& = 16 \cdot \sqrt{2} - 10 \cdot \sqrt{2} + \sqrt{24} + 3 \cdot \sqrt{6}\\& = 16 \cdot \sqrt{2} - 10 \cdot \sqrt{2} + 2 \cdot \sqrt{6} + 3 \cdot \sqrt{6}\\& = 6 \cdot \sqrt{2} + 2 \cdot \sqrt{6} + 3 \cdot \sqrt{6}\\& = \left(2 \cdot \sqrt{6} + 6 \cdot \sqrt{2}\right) + 3 \cdot \sqrt{6}\\& = 5 \cdot \sqrt{6} + 6 \cdot \sqrt{2}\end{aligned}\]