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How do you rationalize the denominator and simplify $\frac{10}{\sqrt[3]{7}}$ $10/root3(7)$ ?

1 Answer

Sep 28, 2015

$\frac{10}{7} \sqrt[3]{49}$ $10/7root(3)(49)$

Explanation:

$\frac{10}{\sqrt[3]{7}}$ $10/root(3)(7)$

$XXX = \frac{10}{\sqrt[3]{7}} \cdot \frac{\sqrt[3]{7}}{\sqrt[3]{7}} \cdot \frac{\sqrt[3]{7}}{\sqrt[3]{7}}$ $color(white)("XXX")=10/root(3)(7)*root(3)(7)/root(3)(7)*root(3)(7)/(root(3)(7)$

$XXX = \frac{10 {(\sqrt[3]{7})}^{2}}{{(\sqrt[3]{7})}^{3}}$ $color(white)("XXX")=(10(root(3)(7))^2)/((root(3)(7))^3)$

$XXX = \frac{10 (\sqrt[3]{7^{2}})}{7}$ $color(white)("XXX")=(10(root(3)(7^2)))/(7)$

$XXX = \frac{10 (\sqrt[3]{49})}{7}$ $color(white)("XXX")=(10(root(3)(49)))/7$

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