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

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

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

simplify

Decimal Notation

1.18920 \dots

Solution steps

Apply radical rule:

= 2^{\frac{1}{5}} \cdot 2^{\frac{1}{20}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2^{\frac{1}{5}} \cdot 2^{\frac{1}{20}} = 2^{\frac{1}{5} + \frac{1}{20}}

= 2^{\frac{1}{5} + \frac{1}{20}}

\frac{1}{5} + \frac{1}{20} = \frac{1}{4}

= 2^{\frac{1}{4}}

Apply exponent rule:

\frac{x ^{2} - 3 x - 4}{x - 4}

\frac{4 x ^{3} y ^{6}}{10 x ^{3} y ^{3}}

lo g_{\frac{1}{16}} (4)

(21)^{2}

\frac{1}{9 x ^{2} - 25} - \frac{1}{6 x + 10}

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