Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[8+\frac{\sqrt{3\sqrt{6\times 3}}}{\frac{8}{}}\]
Simplify \(6\times 3\) to \(18\).
\[8+\frac{\sqrt{3\sqrt{18}}}{\frac{8}{}}\]
Simplify \(\sqrt{18}\) to \(3\sqrt{2}\).
\[8+\frac{\sqrt{3\times 3\sqrt{2}}}{\frac{8}{}}\]
Simplify \(3\times 3\sqrt{2}\) to \(9\sqrt{2}\).
\[8+\frac{\sqrt{9\sqrt{2}}}{\frac{8}{}}\]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[8+\frac{\sqrt{9}\sqrt{\sqrt{2}}}{\frac{8}{}}\]
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[8+\frac{3\sqrt{\sqrt{2}}}{\frac{8}{}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[8+\frac{3\times {2}^{\frac{1\times 1}{2\times 2}}}{\frac{8}{}}\]
Simplify \(1\times 1\) to \(1\).
\[8+\frac{3\sqrt[2\times 2]{2}}{\frac{8}{}}\]
Simplify \(2\times 2\) to \(4\).
\[8+\frac{3\sqrt[4]{2}}{\frac{8}{}}\]
Invert and multiply.
\[8+3\sqrt[4]{2}\times \frac{1}{8}\]
Simplify \(3\sqrt[4]{2}\times \frac{1}{8}\) to \(\frac{3\sqrt[4]{2}}{8}\).
\[8+\frac{3\sqrt[4]{2}}{8}\]
Decimal Form: 8.445953
8+(3*2^(1/4))/8
