What is sqrt(\sqrt[3]{1000/64)} ?

The solution to sqrt(\sqrt[3]{1000/64)} is \sqrt[6]{125/8}

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simplify sqrt(\sqrt[3]{1000/64)}

simplify

Decimal Notation

1.58113 \dots

Solution steps

Apply radical rule:

= ((\frac{1000}{64})^{\frac{1}{3}})^{\frac{1}{2}}

Apply exponent rule:

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

= (\frac{1000}{64})^{\frac{1}{3} \cdot \frac{1}{2}}

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

= (\frac{1000}{64})^{\frac{1}{6}}

\frac{1000}{64} = \frac{125}{8}

0.68 \cdot 1 0^{- 3} \cdot 45

e^{- \frac{x}{2} = \frac{0.2}{1.2}}

e^{t x} (e^{t})

e^{- 2} (x^{2} + 2 y^{2} + 4 x y - 2 y - 4 x + 1)

What is sqrt(\sqrt[3]{1000/64)} ?
The solution to sqrt(\sqrt[3]{1000/64)} is \sqrt[6]{125/8}