Question

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

Answer

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

Solution


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

Decimal Form: 5.565085