What is \sqrt[3]{\sqrt[4]{\sqrt[5]{2}}} ?

The solution to \sqrt[3]{\sqrt[4]{\sqrt[5]{2}}} is \sqrt[60]{2}

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simplify \sqrt[3]{\sqrt[4]{\sqrt[5]{2}}}

simplify

3452

602

Decimal

1.01161 \dots

Solution steps

3452

452 : 202

= 3202

Apply radical rule:

n a = a^{\frac{1}{n}}

= (2^{\frac{1}{20}})^{\frac{1}{3}}

Apply exponent rule:

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

= 2^{\frac{1}{20} \cdot \frac{1}{3}}

\frac{1}{20} \cdot \frac{1}{3} = \frac{1}{60}

= 2^{\frac{1}{60}}

a^{\frac{1}{n}} = n a

= 602

3.3 \cdot 1 0^{- 3}

\frac{11}{43}

cos (2 t) e^{- t} e^{- s t}

\frac{0. 5 ^{2}}{2 !} e^{- 0.5}

(cos (x))^{2} \cdot (sin (x))^{2}

What is \sqrt[3]{\sqrt[4]{\sqrt[5]{2}}} ?
The solution to \sqrt[3]{\sqrt[4]{\sqrt[5]{2}}} is \sqrt[60]{2}