What is \sqrt[3]{\sqrt[5]{125}} ?

The solution to \sqrt[3]{\sqrt[5]{125}} is \sqrt[5]{5}

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simplify \sqrt[3]{\sqrt[5]{125}}

simplify

Decimal Notation

1.37972 \dots

Solution steps

Apply radical rule:

= (12 5^{\frac{1}{5}})^{\frac{1}{3}}

Apply exponent rule:

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

= 12 5^{\frac{1}{5} \cdot \frac{1}{3}}

\frac{1}{5} \cdot \frac{1}{3} = \frac{1}{15}

= 12 5^{\frac{1}{15}}

Factor the number:

125 = 5^{3}

Apply exponent rule:

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

8.639 \cdot 1 0^{8} \cdot e^{- \frac{13639}{8.314 \cdot 0.30815}}

3 e^{- x}

1 0^{- 5}

\frac{137}{14}

What is \sqrt[3]{\sqrt[5]{125}} ?
The solution to \sqrt[3]{\sqrt[5]{125}} is \sqrt[5]{5}