√6+3/√5-√3
You asked:
Evaluate the expression: \(\sqrt{6} + \frac{3}{\sqrt{5}} - \sqrt{3}\)
MathBot Answer:
\[\sqrt{6} + \frac{3}{\sqrt{5}} - \sqrt{3} = - \sqrt{3} + \frac{3 \sqrt{5}}{5} + \sqrt{6} \approx 2.05907972171417462251534193443878\]
\[\begin{aligned}\sqrt{6} + \frac{3}{\sqrt{5}} - \sqrt{3}& = \sqrt{6} + 3 \cdot \frac{1}{\sqrt{5}} - \sqrt{3}\\& = \sqrt{6} + \frac{3}{5} \cdot \sqrt{5} - \sqrt{3}\\& = \left(\sqrt{6} + \frac{3}{5} \cdot \sqrt{5}\right) - \sqrt{3}\\& = \sqrt{6} - \sqrt{3} + \frac{3}{5} \cdot \sqrt{5}\end{aligned}\]