What is sqrt(\sqrt[3]{\sqrt[3]{2\sqrt{2)}}} ?

The solution to sqrt(\sqrt[3]{\sqrt[3]{2\sqrt{2)}}} is \sqrt[12]{2}

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simplify sqrt(\sqrt[3]{\sqrt[3]{2\sqrt{2)}}}

simplify

Decimal Notation

1.05946 \dots

Solution steps

Apply radical rule:

= ((22)^{\frac{1}{9}})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (22)^{\frac{1}{9} \cdot \frac{1}{2}}

\frac{1}{9} \cdot \frac{1}{2} = \frac{1}{18}

= (22)^{\frac{1}{18}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

= 2^{\frac{1}{18} + \frac{1}{36}}

Join

\frac{1}{18} + \frac{1}{36} : \frac{1}{12}

\frac{x ^{2} + y ^{2}}{x ^{2} + y ^{2} + z ^{2}}

\frac{3}{2 3} \cdot \frac{3}{3}

e^{- (\frac{x}{2})^{2}}

3 \cdot \frac{1}{4} \cdot e^{- 4 \cdot \frac{1}{4}}

What is sqrt(\sqrt[3]{\sqrt[3]{2\sqrt{2)}}} ?
The solution to sqrt(\sqrt[3]{\sqrt[3]{2\sqrt{2)}}} is \sqrt[12]{2}