How do you simplify $\sqrt[3]{96}$ $root(3)96$ ?

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Answer 1 · 2016-05-04T00:35:28

$\sqrt[3]{96} = 2 \sqrt[3]{12}$ $root(3)(96)=2root(3)(12)$

Using the fact that for $a, b \geq 0$ $a, b >= 0$ we have $\sqrt[n]{a b} = \sqrt[n]{a} \cdot \sqrt[n]{b}$ $root(n)(ab) = root(n)(a)*root(n)(b)$ :

$\sqrt[3]{96} = \sqrt[3]{8 \cdot 12}$ $root(3)(96) = root(3)(8*12)$

$= \sqrt[3]{8} \cdot \sqrt[3]{12}$ $=root(3)(8)*root(3)(12)$

$= \sqrt[3]{2^{3}} \cdot \sqrt[3]{12}$ $=root(3)(2^3)*root(3)(12)$

$= 2 \sqrt[3]{12}$ $=2root(3)(12)$

How do you simplify root(3)963√96root(3)96?