$\sqrt{12}$- $\sqrt{18}$+ $\sqrt{8}$- $\sqrt{3}$
You asked:
Evaluate the expression: \(\sqrt{12} - \sqrt{18} + \sqrt{8} - \sqrt{3}\)
MathBot Answer:
\[\sqrt{12} - \sqrt{18} + \sqrt{8} - \sqrt{3} = - \sqrt{2} + \sqrt{3} \approx 0.31783724519578224472575761729617\]
\[\begin{aligned}\sqrt{12} - \sqrt{18} + \sqrt{8} - \sqrt{3}& = 2 \cdot \sqrt{3} - \sqrt{18} + \sqrt{8} - \sqrt{3}\\& = 2 \cdot \sqrt{3} - 3 \cdot \sqrt{2} + \sqrt{8} - \sqrt{3}\\& = 2 \cdot \sqrt{3} - 3 \cdot \sqrt{2} + 2 \cdot \sqrt{2} - \sqrt{3}\\& = \left(-3 \cdot \sqrt{2} + 2 \cdot \sqrt{3}\right) + 2 \cdot \sqrt{2} - \sqrt{3}\\& = \left(- \sqrt{2} + 2 \cdot \sqrt{3}\right) - \sqrt{3}\\& = \sqrt{3} - \sqrt{2}\end{aligned}\]