2√12−√27+5√75
You asked:
Evaluate the expression: \(2 \cdot \sqrt{12} - \sqrt{27} + 5 \cdot \sqrt{75}\)
MathBot Answer:
\[2 \cdot \sqrt{12} - \sqrt{27} + 5 \cdot \sqrt{75} = 26 \sqrt{3} \approx 45.03332099679080963171360487915268\]
\[\begin{aligned}2 \cdot \sqrt{12} - \sqrt{27} + 5 \cdot \sqrt{75}& = 2 \cdot 2 \cdot \sqrt{3} - \sqrt{27} + 5 \cdot \sqrt{75}\\& = 4 \cdot \sqrt{3} - \sqrt{27} + 5 \cdot \sqrt{75}\\& = 4 \cdot \sqrt{3} - 3 \cdot \sqrt{3} + 5 \cdot \sqrt{75}\\& = 4 \cdot \sqrt{3} - 3 \cdot \sqrt{3} + 5 \cdot 5 \cdot \sqrt{3}\\& = 4 \cdot \sqrt{3} - 3 \cdot \sqrt{3} + 25 \cdot \sqrt{3}\\& = \sqrt{3} + 25 \cdot \sqrt{3}\\& = 26 \cdot \sqrt{3}\end{aligned}\]