Simplify \(789\times 42\) to \(33138\).
\[789\sqrt{\frac{789}{33138}}\]
Simplify \(\sqrt{\frac{789}{33138}}\) to \(\frac{\sqrt{789}}{\sqrt{33138}}\).
\[789\times \frac{\sqrt{789}}{\sqrt{33138}}\]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[789\times \frac{\sqrt{789}}{\sqrt{33138}\sqrt{1}}\]
Simplify \(\sqrt{33138}\) to \(3\sqrt{3682}\).
\[789\times \frac{\sqrt{789}}{3\sqrt{3682}\sqrt{1}}\]
Simplify \(\sqrt{1}\) to \(1\).
\[789\times \frac{\sqrt{789}}{3\sqrt{3682}\times 1}\]
Simplify \(3\sqrt{3682}\times 1\) to \(3\sqrt{3682}\).
\[789\times \frac{\sqrt{789}}{3\sqrt{3682}}\]
Rationalize the denominator: \(789\times \frac{\sqrt{789}}{3\sqrt{3682}} \cdot \frac{\sqrt{3682}}{\sqrt{3682}}=\frac{789\sqrt{789}\sqrt{3682}}{3\times 3682}\).
\[\frac{789\sqrt{789}\sqrt{3682}}{3\times 3682}\]
Simplify \(789\sqrt{789}\sqrt{3682}\) to \(789\sqrt{2905098}\).
\[\frac{789\sqrt{2905098}}{3\times 3682}\]
Simplify \(\sqrt{2905098}\) to \(263\sqrt{42}\).
\[\frac{789\times 263\sqrt{42}}{3\times 3682}\]
Simplify \(789\times 263\sqrt{42}\) to \(207507\sqrt{42}\).
\[\frac{207507\sqrt{42}}{3\times 3682}\]
Simplify \(3\times 3682\) to \(11046\).
\[\frac{207507\sqrt{42}}{11046}\]
Simplify.
\[\frac{263\sqrt{42}}{14}\]
Decimal Form: 121.745343
(263*sqrt(42))/14
