√3+√27/√2
You asked:
Evaluate the expression: \(\sqrt{3} + \frac{\sqrt{27}}{\sqrt{2}}\)
MathBot Answer:
\[\sqrt{3} + \frac{\sqrt{27}}{\sqrt{2}} = \sqrt{3} + \frac{3 \sqrt{6}}{2} \approx 5.40628542174364444082337245356471\]
\[\begin{aligned}\sqrt{3} + \frac{\sqrt{27}}{\sqrt{2}}& = \sqrt{3} + \sqrt{27} \cdot \frac{1}{\sqrt{2}}\\& = \sqrt{3} + 3 \cdot \sqrt{3} \cdot \frac{1}{\sqrt{2}}\\& = \sqrt{3} + \frac{3}{2} \cdot \sqrt{6}\end{aligned}\]