Question

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

Answer

$$(8+)/(3*2^(1/4))$$

Solution


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