How do you multiply $\sqrt[3]{a} (\sqrt[3]{a^{2}} + \sqrt[3]{81 a^{2}})$ $root3a (root3(a^2) + root3(81a^2))$ ?

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How do you multiply $\sqrt[3]{a} (\sqrt[3]{a^{2}} + \sqrt[3]{81 a^{2}})$ $root3a (root3(a^2) + root3(81a^2))$ ?

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Answer 1 · 2015-10-02T17:34:43

I found: $a (1 + 3 \sqrt[3]{3})$ $a(1+3root3(3))$

Explanation:

We can multiply first:
$\sqrt[3]{a} \cdot \sqrt[3]{a^{2}} + \sqrt[3]{a} \cdot \sqrt[3]{81 a^{2}} =$ $root3(a)*root3(a^2)+root3(a)*root3(81a^2)=$ and rearrange:
$= \sqrt[3]{a \cdot a^{2}} + \sqrt[3]{a \cdot 81 a^{2}} =$ $=root3(a*a^2)+root3(a*81a^2)=$
$= \sqrt[3]{a^{3}} + \sqrt[3]{81 a^{3}} =$ $=root3(a^3)+root3(81a^3)=$ taking cube roots:
$= a + a \sqrt[3]{81} = a + a \sqrt[3]{27 \cdot 3} = = a + 3 a \sqrt[3]{3} =$ $=a+aroot3(81)=a+aroot3(27*3)==a+3aroot3(3)=$
$= a (1 + 3 \sqrt[3]{3})$ $=a(1+3root3(3))$

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How do you multiply $\sqrt[3]{a} (\sqrt[3]{a^{2}} + \sqrt[3]{81 a^{2}})$ $root3a (root3(a^2) + root3(81a^2))$ ?

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How do you multiply 3√a(3√a2+3√81a2)root3a (root3(a^2) + root3(81a^2)) ?

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How do you multiply $\sqrt[3]{a} (\sqrt[3]{a^{2}} + \sqrt[3]{81 a^{2}})$ $root3a (root3(a^2) + root3(81a^2))$ ?