Question

$$8+ \sqrt{ 1 \sqrt{ 3 \sqrt{ 4 } } } +$$

Answer

$$8+6^(1/4)+$$

Solution


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