What is \sqrt[4]{\sqrt[5]{sqrt(3)}} ?

The solution to \sqrt[4]{\sqrt[5]{sqrt(3)}} is \sqrt[40]{3}

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simplify \sqrt[4]{\sqrt[5]{sqrt(3)}}

simplify

Decimal Notation

1.02784 \dots

Solution steps

Apply radical rule:

= (3^{\frac{1}{10}})^{\frac{1}{4}}

Apply exponent rule:

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

= 3^{\frac{1}{10} \cdot \frac{1}{4}}

\frac{1}{10} \cdot \frac{1}{4} = \frac{1}{40}

= 3^{\frac{1}{40}}

3 e^{- 0}

e^{2 x} e^{- 2 x}

e^{- 3 \cdot 0}

(25)^{3}

256

What is \sqrt[4]{\sqrt[5]{sqrt(3)}} ?
The solution to \sqrt[4]{\sqrt[5]{sqrt(3)}} is \sqrt[40]{3}