Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{2}}-\frac{\sqrt{3}}{2}\]
Rationalize the denominator: \(\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3}\).
\[\frac{\sqrt{3}}{3}+\frac{1}{\sqrt{2}}-\frac{\sqrt{3}}{2}\]
Rationalize the denominator: \(\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}\).
\[\frac{\sqrt{3}}{3}+\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{2}\]
Collect like terms.
\[(\frac{\sqrt{3}}{3}-\frac{\sqrt{3}}{2})+\frac{\sqrt{2}}{2}\]
Simplify.
\[-\frac{\sqrt{3}}{6}+\frac{\sqrt{2}}{2}\]
Decimal Form: 0.418432
-sqrt(3)/6+sqrt(2)/2
