Simplify \(458\times 72\) to \(32976\).
\[458\sqrt{\frac{458}{32976}}\]
Simplify \(\sqrt{\frac{458}{32976}}\) to \(\frac{\sqrt{458}}{\sqrt{32976}}\).
\[458\times \frac{\sqrt{458}}{\sqrt{32976}}\]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[458\times \frac{\sqrt{458}}{\sqrt{32976}\sqrt{1}}\]
Simplify \(\sqrt{32976}\) to \(12\sqrt{229}\).
\[458\times \frac{\sqrt{458}}{12\sqrt{229}\sqrt{1}}\]
Simplify \(\sqrt{1}\) to \(1\).
\[458\times \frac{\sqrt{458}}{12\sqrt{229}\times 1}\]
Simplify \(12\sqrt{229}\times 1\) to \(12\sqrt{229}\).
\[458\times \frac{\sqrt{458}}{12\sqrt{229}}\]
Rationalize the denominator: \(458\times \frac{\sqrt{458}}{12\sqrt{229}} \cdot \frac{\sqrt{229}}{\sqrt{229}}=\frac{458\sqrt{458}\sqrt{229}}{12\times 229}\).
\[\frac{458\sqrt{458}\sqrt{229}}{12\times 229}\]
Simplify \(458\sqrt{458}\sqrt{229}\) to \(458\sqrt{104882}\).
\[\frac{458\sqrt{104882}}{12\times 229}\]
Simplify \(\sqrt{104882}\) to \(229\sqrt{2}\).
\[\frac{458\times 229\sqrt{2}}{12\times 229}\]
Simplify \(458\times 229\sqrt{2}\) to \(104882\sqrt{2}\).
\[\frac{104882\sqrt{2}}{12\times 229}\]
Simplify \(12\times 229\) to \(2748\).
\[\frac{104882\sqrt{2}}{2748}\]
Simplify.
\[\frac{229\sqrt{2}}{6}\]
Decimal Form: 53.975818
(229*sqrt(2))/6
