Question

$$3+ \sqrt{ 6 \sqrt{ 8 \sqrt{ 9 } } } +$$

Answer

$$3+2*sqrt(3)*6^(1/4)+$$

Solution


Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[3+\sqrt{6\sqrt{8\times 3}}+\]
Simplify  \(8\times 3\)  to  \(24\).
\[3+\sqrt{6\sqrt{24}}+\]
Simplify  \(\sqrt{24}\)  to  \(2\sqrt{6}\).
\[3+\sqrt{6\times 2\sqrt{6}}+\]
Simplify  \(6\times 2\sqrt{6}\)  to  \(12\sqrt{6}\).
\[3+\sqrt{12\sqrt{6}}+\]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[3+\sqrt{12}\sqrt{\sqrt{6}}+\]
Simplify  \(\sqrt{12}\)  to  \(2\sqrt{3}\).
\[3+2\sqrt{3}\sqrt{\sqrt{6}}+\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[3+2\sqrt{3}\times {6}^{\frac{1\times 1}{2\times 2}}+\]
Simplify  \(1\times 1\)  to  \(1\).
\[3+2\sqrt{3}\sqrt[2\times 2]{6}+\]
Simplify  \(2\times 2\)  to  \(4\).
\[3+2\sqrt{3}\sqrt[4]{6}+\]