What is \sqrt[3]{sqrt(72+6\sqrt{18)}} ?

The solution to \sqrt[3]{sqrt(72+6\sqrt{18)}} is \sqrt[6]{72+18sqrt(2)}

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simplify \sqrt[3]{sqrt(72+6\sqrt{18)}}

simplify

Decimal Notation

2.14520 \dots

Solution steps

Apply radical rule:

= ((72 + 618)^{\frac{1}{2}})^{\frac{1}{3}}

Apply exponent rule:

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

= (72 + 618)^{\frac{1}{2} \cdot \frac{1}{3}}

\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}

= (72 + 618)^{\frac{1}{6}}

618 = 182

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What is \sqrt[3]{sqrt(72+6\sqrt{18)}} ?
The solution to \sqrt[3]{sqrt(72+6\sqrt{18)}} is \sqrt[6]{72+18sqrt(2)}