$\sqrt{6}$ (3 $\sqrt{8}$ - 10 $\sqrt{54}$ )
You asked:
Evaluate the expression: \(\sqrt{6} \left(3 \sqrt{8} - 10 \sqrt{54}\right)\)
MathBot Answer:
\[\sqrt{6} \left(3 \sqrt{8} - 10 \sqrt{54}\right) = \sqrt{6} \left(- 30 \sqrt{6} + 6 \sqrt{2}\right) \approx -159.21539030917347247767064390192953\]
\[\begin{aligned}\sqrt{6} \left(3 \sqrt{8} - 10 \sqrt{54}\right)& = \sqrt{6} \cdot \left(3 \cdot \sqrt{8} - 10 \cdot \sqrt{54}\right)\\& = \sqrt{6} \cdot \left(3 \cdot 2 \cdot \sqrt{2} - 10 \cdot \sqrt{54}\right)\\& = \sqrt{6} \cdot \left(6 \cdot \sqrt{2} - 10 \cdot \sqrt{54}\right)\\& = \sqrt{6} \cdot \left(6 \cdot \sqrt{2} - 10 \cdot 3 \cdot \sqrt{6}\right)\\& = \sqrt{6} \cdot \left(6 \cdot \sqrt{2} - 30 \cdot \sqrt{6}\right)\\& = \sqrt{6} \cdot \left(-30 \cdot \sqrt{6} + 6 \cdot \sqrt{2}\right)\end{aligned}\]