Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[6+\sqrt{2\sqrt{4}\sqrt{\sqrt{6}}}\]
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[6+\sqrt{2\times 2\sqrt{\sqrt{6}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[6+\sqrt{2\times 2\times {6}^{\frac{1\times 1}{2\times 2}}}\]
Simplify \(1\times 1\) to \(1\).
\[6+\sqrt{2\times 2\sqrt[2\times 2]{6}}\]
Simplify \(2\times 2\) to \(4\).
\[6+\sqrt{4\sqrt[4]{6}}\]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[6+\sqrt{4}\sqrt{\sqrt[4]{6}}\]
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[6+2\sqrt{\sqrt[4]{6}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[6+2\times {6}^{\frac{1\times 1}{4\times 2}}\]
Simplify \(1\times 1\) to \(1\).
\[6+2\sqrt[4\times 2]{6}\]
Simplify \(4\times 2\) to \(8\).
\[6+2\sqrt[8]{6}\]
Decimal Form: 8.502067
6+2*6^(1/8)
