Practice Problems

\(\textbf{1)}\) \(\sqrt[3]{2}\cdot\sqrt[3]{5}\)

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The answer is \(\sqrt[3]{10}\)

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\(\,\,\,\,\,\,\,\,\,\sqrt[3]{2} \cdot \sqrt[3]{5}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{2 \cdot 5}\)
\(\,\,\,\,\,\,\,\,\,\)The answer is \(\sqrt[3]{10}\)

 

\(\textbf{2)}\) \(\sqrt[3]{2} \cdot \sqrt[3]{4}\)

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The answer is \( 2 \)

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\(\,\,\,\,\,\,\,\,\sqrt[3]{2} \cdot \sqrt[3]{4}\)
\(\,\,\,\,\,\,\,\,\sqrt[3]{2 \cdot 4}\)
\(\,\,\,\,\,\,\,\,\sqrt[3]{8}\)
\(\,\,\,\,\,\,\,\,\)The answer is \( 2 \)

 

\(\textbf{3)}\) \(\sqrt[3]{3} \cdot \sqrt[3]{9}\)

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The answer is \( 3 \)

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\(\,\,\,\,\,\,\,\,\,\sqrt[3]{3} \cdot \sqrt[3]{9}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{3 \cdot 9}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{27}\)
\(\,\,\,\,\,\,\,\,\,\)The answer is \( 3 \)

 

\(\textbf{4)}\) \(\sqrt[3]{12}\cdot\sqrt[3]{2}\)

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The answer is \(2\sqrt[3]{3}\)

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\(\,\,\,\,\,\,\,\,\,\sqrt[3]{12} \cdot \sqrt[3]{2}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{2 \cdot 2 \cdot 3} \cdot \sqrt[3]{2}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{2 \cdot 2 \cdot 2 \cdot 3}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{8 \cdot 3}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{8} \cdot \sqrt[3]{3}\)
\(\,\,\,\,\,\,\,\,\,2 \cdot \sqrt[3]{3}\)
\(\,\,\,\,\,\,\,\,\,\)The answer is \(2 \sqrt[3]{3}\)

 

\(\textbf{5)}\) \(\sqrt[3]{75}\cdot\sqrt[3]{9}\)

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The answer is \(3\sqrt[3]{25}\)

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\(\,\,\,\,\,\,\,\,\,\sqrt[3]{75} \cdot \sqrt[3]{9}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{3 \cdot 5 \cdot 5} \cdot \sqrt[3]{3 \cdot 3}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{3 \cdot 3 \cdot 3 \cdot 5 \cdot 5}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{27 \cdot 25}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{27} \cdot \sqrt[3]{25}\)
\(\,\,\,\,\,\,\,\,\,3 \cdot \sqrt[3]{25}\)
\(\,\,\,\,\,\,\,\,\,\)The answer is \(3 \sqrt[3]{25}\)

 

\(\textbf{6)}\) \(\sqrt[3]{7}\cdot\sqrt[3]{14}\)

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The answer is \(\sqrt[3]{98}\)

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\(\,\,\,\,\,\,\,\,\,\sqrt[3]{7} \cdot \sqrt[3]{14}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{7} \cdot \sqrt[3]{2 \cdot 7}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{2 \cdot 7 \cdot 7 }\)
\(\,\,\,\,\,\,\,\,\,\)The answer is \(\sqrt[3]{98}\)

 

\(\textbf{7)}\) \( \sqrt[3]{10}\cdot\sqrt[3]{5}\)

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The answer is \(\sqrt[3]{50}\)

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\(\,\,\,\,\,\,\,\,\,\sqrt[3]{10} \cdot \sqrt[3]{5}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{2 \cdot 5} \cdot \sqrt[3]{5}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{2 \cdot 5 \cdot 5 }\)
\(\,\,\,\,\,\,\,\,\,\) The answer is \(\sqrt[3]{50}\)

 

\(\textbf{8)}\) \( \sqrt[3]{8}\cdot\sqrt[3]{12}\)

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The answer is \(2\sqrt[3]{12}\)

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\(\,\,\,\,\,\,\,\,\,\sqrt[3]{8} \cdot \sqrt[3]{12}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{2 \cdot 2 \cdot 2} \cdot \sqrt[3]{2 \cdot 2 \cdot 3}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 }\)
\(\,\,\,\,\,\,\,\,\,\) The answer is \(2\sqrt[3]{12}\)

 

\(\textbf{9)}\) \( \sqrt[3]{6}\cdot\sqrt[3]{4}\)

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The answer is \(2\sqrt[3]{3}\)

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\(\,\,\,\,\,\,\,\,\,\sqrt[3]{6} \cdot \sqrt[3]{4}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{2 \cdot 3} \cdot \sqrt[3]{2 \cdot 2}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{2 \cdot 3 \cdot 2 \cdot 2 }\)
\(\,\,\,\,\,\,\,\,\,\) The answer is \(2\sqrt[3]{3}\)

 

\(\textbf{10)}\) \( \sqrt[3]{15}\cdot\sqrt[3]{9}\)

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The answer is \(3\sqrt[3]{5}\)

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\(\,\,\,\,\,\,\,\,\,\sqrt[3]{15} \cdot \sqrt[3]{9}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{3 \cdot 5} \cdot \sqrt[3]{3 \cdot 3}\)
\(\,\,\,\,\,\,\,\,\,\sqrt[3]{3 \cdot 5 \cdot 3 \cdot 3}\)
\(\,\,\,\,\,\,\,\,\,\) The answer is \(3\sqrt[3]{5}\)

 

See Related Pages\(\)

\(\bullet\text{Cube Root Multiplication Calculator }\)
\(\,\,\,\,\,\,\,\,\text{(Symbolab.com)}\)

\(\bullet\text{ Simplifying Cube Roots}\)
\(\,\,\,\,\,\,\,\,\sqrt[3]{48}=2\sqrt[3]6…\)