What is \sqrt[3]{sqrt(\sqrt{7)}} ?

The solution to \sqrt[3]{sqrt(\sqrt{7)}} is \sqrt[12]{7}

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simplify \sqrt[3]{sqrt(\sqrt{7)}}

simplify

Decimal Notation

1.17604 \dots

Solution steps

Apply radical rule:

= (7^{\frac{1}{4}})^{\frac{1}{3}}

Apply exponent rule:

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

= 7^{\frac{1}{4} \cdot \frac{1}{3}}

\frac{1}{4} \cdot \frac{1}{3} = \frac{1}{12}

= 7^{\frac{1}{12}}

6.4 \cdot 1 0^{- 2}

9 x^{3} (3 x^{5})

25.2 \cdot 1 0^{- 3}

25.2 \cdot 1 0^{- 4}

What is \sqrt[3]{sqrt(\sqrt{7)}} ?
The solution to \sqrt[3]{sqrt(\sqrt{7)}} is \sqrt[12]{7}