Simplify \(360\times 9\) to \(3240\).
\[360\sqrt{\frac{9}{3240}}\]
Simplify \(\sqrt{\frac{9}{3240}}\) to \(\frac{\sqrt{9}}{\sqrt{3240}}\).
\[360\times \frac{\sqrt{9}}{\sqrt{3240}}\]
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[360\times \frac{3}{\sqrt{3240}}\]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[360\times \frac{3}{\sqrt{3240}\sqrt{1}}\]
Simplify \(\sqrt{3240}\) to \(18\sqrt{10}\).
\[360\times \frac{3}{18\sqrt{10}\sqrt{1}}\]
Simplify \(\sqrt{1}\) to \(1\).
\[360\times \frac{3}{18\sqrt{10}\times 1}\]
Simplify \(18\sqrt{10}\times 1\) to \(18\sqrt{10}\).
\[360\times \frac{3}{18\sqrt{10}}\]
Rationalize the denominator: \(360\times \frac{3}{18\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}=\frac{360\times 3\sqrt{10}}{18\times 10}\).
\[\frac{360\times 3\sqrt{10}}{18\times 10}\]
Simplify \(360\times 3\sqrt{10}\) to \(1080\sqrt{10}\).
\[\frac{1080\sqrt{10}}{18\times 10}\]
Simplify \(18\times 10\) to \(180\).
\[\frac{1080\sqrt{10}}{180}\]
Simplify.
\[6\sqrt{10}\]
Decimal Form: 18.973666
6*sqrt(10)
