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