Simplify \({7}^{2}\) to \(49\).
\[\frac{3\sqrt{49\times 3\sqrt{7}}}{\sqrt{7}}\]
Simplify \(49\times 3\sqrt{7}\) to \(147\sqrt{7}\).
\[\frac{3\sqrt{147\sqrt{7}}}{\sqrt{7}}\]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[\frac{3\sqrt{147}\sqrt{\sqrt{7}}}{\sqrt{7}}\]
Simplify \(\sqrt{147}\) to \(7\sqrt{3}\).
\[\frac{3\times 7\sqrt{3}\sqrt{\sqrt{7}}}{\sqrt{7}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{3\times 7\sqrt{3}\times {7}^{\frac{1\times 1}{2\times 2}}}{\sqrt{7}}\]
Simplify \(1\times 1\) to \(1\).
\[\frac{3\times 7\sqrt{3}\sqrt[2\times 2]{7}}{\sqrt{7}}\]
Simplify \(2\times 2\) to \(4\).
\[\frac{3\times 7\sqrt{3}\sqrt[4]{7}}{\sqrt{7}}\]
Simplify \(3\times 7\sqrt{3}\sqrt[4]{7}\) to \(21\sqrt{3}\sqrt[4]{7}\).
\[\frac{21\sqrt{3}\sqrt[4]{7}}{\sqrt{7}}\]
Regroup terms.
\[\frac{21\sqrt[4]{7}\sqrt{3}}{\sqrt{7}}\]
Rationalize the denominator: \(\frac{21\sqrt[4]{7}\sqrt{3}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}=\frac{21\sqrt[4]{7}\sqrt{3}\sqrt{7}}{7}\).
\[\frac{21\sqrt[4]{7}\sqrt{3}\sqrt{7}}{7}\]
Simplify \(21\sqrt[4]{7}\sqrt{3}\sqrt{7}\) to \(21\sqrt[4]{7}\sqrt{21}\).
\[\frac{21\sqrt[4]{7}\sqrt{21}}{7}\]
Simplify square root.
\[\frac{21\sqrt{21}\sqrt[4]{7}}{7}\]
Regroup terms.
\[\frac{21\sqrt[4]{7}\sqrt{21}}{7}\]
Decimal Form: 22.361731
(21*7^(1/4)*sqrt(21))/7
