Rationalize the denominator: \(\frac{3\sqrt{5}}{3+\sqrt{6}} \cdot \frac{3-\sqrt{6}}{3-\sqrt{6}}=\frac{9\sqrt{5}-3\sqrt{30}}{{3}^{2}-{\sqrt{6}}^{2}}\).
\[\frac{9\sqrt{5}-3\sqrt{30}}{{3}^{2}-{\sqrt{6}}^{2}}\]
Factor out the common term \(3\).
\[\frac{3(3\sqrt{5}-\sqrt{30})}{{3}^{2}-{\sqrt{6}}^{2}}\]
Simplify \({3}^{2}\) to \(9\).
\[\frac{3(3\sqrt{5}-\sqrt{30})}{9-{\sqrt{6}}^{2}}\]
Use this rule: \({\sqrt{x}}^{2}=x\).
\[\frac{3(3\sqrt{5}-\sqrt{30})}{9-6}\]
Simplify \(9-6\) to \(3\).
\[\frac{3(3\sqrt{5}-\sqrt{30})}{3}\]
Cancel \(3\).
\[3\sqrt{5}-\sqrt{30}\]
Decimal Form: 1.230978
3*sqrt(5)-sqrt(30)
