Simplify \(\sqrt{\frac{8}{}}\) to \(\frac{\sqrt{8}}{\sqrt{}}\).
\[8+\sqrt{2\sqrt{7\sqrt{9\times \frac{\sqrt{8}}{\sqrt{}}}}}+\]
Simplify \(\sqrt{8}\) to \(2\sqrt{2}\).
\[8+\sqrt{2\sqrt{7\sqrt{9\times \frac{2\sqrt{2}}{\sqrt{}}}}}+\]
Rationalize the denominator: \(9\times \frac{2\sqrt{2}}{\sqrt{}} \cdot \frac{\sqrt{}}{\sqrt{}}=9\times 2\sqrt{2}\sqrt{}\).
\[8+\sqrt{2\sqrt{7\sqrt{9\times 2\sqrt{2}\sqrt{}}}}+\]
Simplify \(9\times 2\sqrt{2}\sqrt{}\) to \(9\times 2\sqrt{2}\).
\[8+\sqrt{2\sqrt{7\sqrt{9\times 2\sqrt{2}}}}+\]
Simplify \(9\times 2\sqrt{2}\) to \(18\sqrt{2}\).
\[8+\sqrt{2\sqrt{7\sqrt{18\sqrt{2}}}}+\]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[8+\sqrt{2\sqrt{7\sqrt{18}\sqrt{\sqrt{2}}}}+\]
Simplify \(\sqrt{18}\) to \(3\sqrt{2}\).
\[8+\sqrt{2\sqrt{7\times 3\sqrt{2}\sqrt{\sqrt{2}}}}+\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[8+\sqrt{2\sqrt{7\times 3\sqrt{2}{(2)}^{\frac{1\times 1}{2\times 2}}}}+\]
Simplify \(1\times 1\) to \(1\).
\[8+\sqrt{2\sqrt{7\times 3\sqrt{2}\sqrt[2\times 2]{2}}}+\]
Simplify \(2\times 2\) to \(4\).
\[8+\sqrt{2\sqrt{7\times 3\sqrt{2}\sqrt[4]{2}}}+\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[8+\sqrt{2\sqrt{7\times 3\sqrt{2}\sqrt[4]{2}\sqrt[4]{}}}+\]
Simplify \(7\times 3\sqrt{2}\sqrt[4]{2}\sqrt[4]{}\) to \(21\sqrt{2}\sqrt[4]{2}\sqrt[4]{}\).
\[8+\sqrt{2\sqrt{21\sqrt{2}\sqrt[4]{2}\sqrt[4]{}}}+\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[8+\sqrt{2\sqrt{21\times {2}^{\frac{3}{4}}\sqrt[4]{}}}+\]
Collect like terms.
\[8+\sqrt{2\sqrt{21\times {2}^{\frac{3}{4}}\sqrt[4]{}}}+1\]
Collect like terms.
\[(8+1)+\sqrt{2\sqrt{21\times {2}^{\frac{3}{4}}\sqrt[4]{}}}\]
Simplify.
\[9+\sqrt{2\sqrt{21\times {2}^{\frac{3}{4}}\sqrt[4]{}}}\]
9+sqrt(2*sqrt(21*2^(3/4)*^(1/4)))
