What is \sqrt[3]{\sqrt[5]{27}} ?

The solution to \sqrt[3]{\sqrt[5]{27}} is \sqrt[5]{3}

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simplify \sqrt[3]{\sqrt[5]{27}}

simplify

Decimal Notation

1.24573 \dots

Solution steps

Apply radical rule:

= (2 7^{\frac{1}{5}})^{\frac{1}{3}}

Apply exponent rule:

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

= 2 7^{\frac{1}{5} \cdot \frac{1}{3}}

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

= 2 7^{\frac{1}{15}}

Factor the number:

27 = 3^{3}

Apply exponent rule:

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

\frac{( - 35 ) ^{7}}{5 ^{7}}

(2 x^{7}) (5 x^{2})

(32) 2

e^{- \frac{15}{10}}

What is \sqrt[3]{\sqrt[5]{27}} ?
The solution to \sqrt[3]{\sqrt[5]{27}} is \sqrt[5]{3}