What is \sqrt[3]{sqrt(5ab)} ?

The solution to \sqrt[3]{sqrt(5ab)} is \sqrt[6]{5}\sqrt[6]{ab}

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simplify \sqrt[3]{sqrt(5ab)}

simplify

Solution steps

Apply radical rule:

= ((5 ab)^{\frac{1}{2}})^{\frac{1}{3}}

Apply exponent rule:

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

assuming

a \geq 0

= (5 ab)^{\frac{1}{2} \cdot \frac{1}{3}}

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

= (5 ab)^{\frac{1}{6}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

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9 m^{2} n^{2} (- 3 m - 2 n)

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(x + 1)^{2} \cdot (x + 2)^{2}

e^{- 2 x} cos (2)

What is \sqrt[3]{sqrt(5ab)} ?
The solution to \sqrt[3]{sqrt(5ab)} is \sqrt[6]{5}\sqrt[6]{ab}