What is \sqrt[6]{\sqrt[3]{2sqrt(2)}} ?

The solution to \sqrt[6]{\sqrt[3]{2sqrt(2)}} is \sqrt[12]{2}

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simplify \sqrt[6]{\sqrt[3]{2sqrt(2)}}

simplify

Decimal Notation

1.05946 \dots

Solution steps

Apply radical rule:

= ((22)^{\frac{1}{3}})^{\frac{1}{6}}

Apply exponent rule:

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

= (22)^{\frac{1}{3} \cdot \frac{1}{6}}

\frac{1}{3} \cdot \frac{1}{6} = \frac{1}{18}

= (22)^{\frac{1}{18}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

Apply exponent rule:

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

= 2^{\frac{1}{18} + \frac{1}{36}}

Join

\frac{1}{18} + \frac{1}{36} : \frac{1}{12}

(3, 1) (- 1, - 1)

10 t \cdot e^{- 5 t}

(x^{4} + y^{4}) (x^{2} y^{2})

0.5 e^{- 2 t} (20 \cdot 1 0^{- 3})

e^{- \frac{1.5 x}{5 x + 3}}

What is \sqrt[6]{\sqrt[3]{2sqrt(2)}} ?
The solution to \sqrt[6]{\sqrt[3]{2sqrt(2)}} is \sqrt[12]{2}