What is \sqrt[4]{\sqrt[3]{sqrt(3)}} ?

The solution to \sqrt[4]{\sqrt[3]{sqrt(3)}} is \sqrt[24]{3}

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simplify \sqrt[4]{\sqrt[3]{sqrt(3)}}

simplify

Decimal Notation

1.04683 \dots

Solution steps

Apply radical rule:

= (3^{\frac{1}{6}})^{\frac{1}{4}}

Apply exponent rule:

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

= 3^{\frac{1}{6} \cdot \frac{1}{4}}

\frac{1}{6} \cdot \frac{1}{4} = \frac{1}{24}

= 3^{\frac{1}{24}}

7.55 \cdot 1 0^{- 5}

616 e^{28} e^{8}

7.55 \cdot 1 0^{- 8}

\frac{66}{35}

What is \sqrt[4]{\sqrt[3]{sqrt(3)}} ?
The solution to \sqrt[4]{\sqrt[3]{sqrt(3)}} is \sqrt[24]{3}