What is (\sqrt[6]{5sqrt(2)-7})^3 ?

The solution to (\sqrt[6]{5sqrt(2)-7})^3 is sqrt(5\sqrt{2)-7}

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simplify (\sqrt[6]{5sqrt(2)-7})^3

simplify

52 - 7

Solution steps

Apply radical rule:

= ((52 - 7)^{\frac{1}{6}})^{3}

Apply exponent rule:

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

= (52 - 7)^{\frac{1}{6} \cdot 3}

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

= (52 - 7)^{\frac{1}{2}}

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

= 52 - 7

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What is (\sqrt[6]{5sqrt(2)-7})^3 ?
The solution to (\sqrt[6]{5sqrt(2)-7})^3 is sqrt(5\sqrt{2)-7}