Cube roots ask what number can be multiplied by itself three times to make the original value. To simplify cube roots, look for perfect cube factors such as \(8\), \(27\), \(64\), \(125\), and \(216\). These practice problems focus on simplifying cube roots by factoring out groups of three matching factors.

Lesson

Practice Problems

Simplify

\(\textbf{1)}\) \( \sqrt[3]{48} \)

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

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\(\,\,\,\,\,\sqrt[3]{48}\)

\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2\cdot2\cdot3}\)

\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2}\cdot\sqrt[3]{2\cdot3}\)

\(\,\,\,\,\,\sqrt[3]{8}\cdot\sqrt[3]{6}\)

\(\,\,\,\,\,2\sqrt[3]{6}\)

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

 

\(\textbf{2)}\) \( \sqrt[3]{24} \)

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

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\(\,\,\,\,\,\sqrt[3]{24}\)

\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2\cdot3}\)

\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2}\cdot\sqrt[3]{3}\)

\(\,\,\,\,\,\sqrt[3]{8}\cdot\sqrt[3]{3}\)

\(\,\,\,\,\,2\sqrt[3]{3}\)

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

 

\(\textbf{3)}\) \( \sqrt[3]{240} \)

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The answer is \( 2\sqrt[3]{30} \)

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\(\,\,\,\,\,\sqrt[3]{240}\)

\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2\cdot2\cdot3\cdot5}\)

\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2}\cdot\sqrt[3]{2\cdot3\cdot5}\)

\(\,\,\,\,\,\sqrt[3]{8}\cdot\sqrt[3]{30}\)

\(\,\,\,\,\,2\sqrt[3]{30}\)

\(\,\,\,\,\,\)The answer is \(2\sqrt[3]{30}\)

 

\(\textbf{4)}\) \( \sqrt[3]{128} \)

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

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\(\,\,\,\,\,\sqrt[3]{128}\)

\(\,\,\,\,\,\sqrt[3]{64\cdot2}\)

\(\,\,\,\,\,\sqrt[3]{64}\cdot\sqrt[3]{2}\)

\(\,\,\,\,\,4\sqrt[3]{2}\)

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

 

\(\textbf{5)}\) \( \sqrt[3]{135} \)

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

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\(\,\,\,\,\,\sqrt[3]{135}\)

\(\,\,\,\,\,\sqrt[3]{3\cdot3\cdot3\cdot5}\)

\(\,\,\,\,\,\sqrt[3]{3\cdot3\cdot3}\cdot\sqrt[3]{5}\)

\(\,\,\,\,\,\sqrt[3]{27}\cdot\sqrt[3]{5}\)

\(\,\,\,\,\,3\sqrt[3]{5}\)

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

 

\(\textbf{6)}\) \( \sqrt[3]{2160} \)

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The answer is \( 6\sqrt[3]{10} \)

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\(\,\,\,\,\,\sqrt[3]{2160}\)

\(\,\,\,\,\,\sqrt[3]{216\cdot10}\)

\(\,\,\,\,\,\sqrt[3]{216}\cdot\sqrt[3]{10}\)

\(\,\,\,\,\,6\sqrt[3]{10}\)

\(\,\,\,\,\,\)The answer is \(6\sqrt[3]{10}\)

 

\(\textbf{7)}\) \( \sqrt[3]{375} \)

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

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\(\,\,\,\,\,\sqrt[3]{375}\)

\(\,\,\,\,\,\sqrt[3]{3\cdot5\cdot5\cdot5}\)

\(\,\,\,\,\,\sqrt[3]{3}\cdot\sqrt[3]{5\cdot5\cdot5}\)

\(\,\,\,\,\,\sqrt[3]{3}\cdot\sqrt[3]{125}\)

\(\,\,\,\,\,5\sqrt[3]{3}\)

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

 

\(\textbf{8)}\) \( \sqrt[3]{960} \)

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The answer is \( 4\sqrt[3]{15} \)

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\(\,\,\,\,\,\sqrt[3]{960}\)

\(\,\,\,\,\,\sqrt[3]{64\cdot15}\)

\(\,\,\,\,\,\sqrt[3]{64}\cdot\sqrt[3]{15}\)

\(\,\,\,\,\,4\sqrt[3]{15}\)

\(\,\,\,\,\,\)The answer is \(4\sqrt[3]{15}\)

 

\(\textbf{9)}\) \( \sqrt[3]{686} \)

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The answer is \( 7\sqrt[3]{2} \)

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\(\,\,\,\,\,\sqrt[3]{686}\)

\(\,\,\,\,\,\sqrt[3]{2\cdot7\cdot7\cdot7}\)

\(\,\,\,\,\,\sqrt[3]{2}\cdot\sqrt[3]{7\cdot7\cdot7}\)

\(\,\,\,\,\,\sqrt[3]{2}\cdot\sqrt[3]{343}\)

\(\,\,\,\,\,7\sqrt[3]{2}\)

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

 

\(\textbf{10)}\) \( \sqrt[3]{54} \)

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

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\(\,\,\,\,\,\sqrt[3]{54}\)

\(\,\,\,\,\,\sqrt[3]{27\cdot2}\)

\(\,\,\,\,\,\sqrt[3]{27}\cdot\sqrt[3]{2}\)

\(\,\,\,\,\,3\sqrt[3]{2}\)

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

 

\(\textbf{11)}\) \( \sqrt[3]{81} \)

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

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\(\,\,\,\,\,\sqrt[3]{81}\)

\(\,\,\,\,\,\sqrt[3]{27\cdot3}\)

\(\,\,\,\,\,\sqrt[3]{27}\cdot\sqrt[3]{3}\)

\(\,\,\,\,\,3\sqrt[3]{3}\)

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

 

\(\textbf{12)}\) \( \sqrt[3]{432} \)

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

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\(\,\,\,\,\,\sqrt[3]{432}\)

\(\,\,\,\,\,\sqrt[3]{216\cdot2}\)

\(\,\,\,\,\,\sqrt[3]{216}\cdot\sqrt[3]{2}\)

\(\,\,\,\,\,6\sqrt[3]{2}\)

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

 

\(\textbf{13)}\) \( \sqrt[3]{1029} \)

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The answer is \( 7\sqrt[3]{3} \)

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\(\,\,\,\,\,\sqrt[3]{1029}\)

\(\,\,\,\,\,\sqrt[3]{343\cdot3}\)

\(\,\,\,\,\,\sqrt[3]{343}\cdot\sqrt[3]{3}\)

\(\,\,\,\,\,7\sqrt[3]{3}\)

\(\,\,\,\,\,\)The answer is \(7\sqrt[3]{3}\)

 

\(\textbf{14)}\) \( \sqrt[3]{625} \)

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

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\(\,\,\,\,\,\sqrt[3]{625}\)

\(\,\,\,\,\,\sqrt[3]{125\cdot5}\)

\(\,\,\,\,\,\sqrt[3]{125}\cdot\sqrt[3]{5}\)

\(\,\,\,\,\,5\sqrt[3]{5}\)

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

 

\(\textbf{15)}\) \( \sqrt[3]{1125} \)

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

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\(\,\,\,\,\,\sqrt[3]{1125}\)

\(\,\,\,\,\,\sqrt[3]{125\cdot9}\)

\(\,\,\,\,\,\sqrt[3]{125}\cdot\sqrt[3]{9}\)

\(\,\,\,\,\,5\sqrt[3]{9}\)

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

 

\(\textbf{16)}\) \( \sqrt[3]{2000} \)

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

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\(\,\,\,\,\,\sqrt[3]{2000}\)

\(\,\,\,\,\,\sqrt[3]{1000\cdot2}\)

\(\,\,\,\,\,\sqrt[3]{1000}\cdot\sqrt[3]{2}\)

\(\,\,\,\,\,10\sqrt[3]{2}\)

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

 

\(\textbf{17)}\) \( \sqrt[3]{250} \)

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

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\(\,\,\,\,\,\sqrt[3]{250}\)

\(\,\,\,\,\,\sqrt[3]{125\cdot2}\)

\(\,\,\,\,\,\sqrt[3]{125}\cdot\sqrt[3]{2}\)

\(\,\,\,\,\,5\sqrt[3]{2}\)

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

 

\(\textbf{18)}\) \( \sqrt[3]{-64} \)

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The answer is \( -4 \)

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\(\,\,\,\,\,\sqrt[3]{-64}\)

\(\,\,\,\,\,\sqrt[3]{(-4)^3}\)

\(\,\,\,\,\,-4\)

\(\,\,\,\,\,\)The answer is \(-4\)

 

\(\textbf{19)}\) \( \sqrt[3]{-250} \)

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The answer is \( -5\sqrt[3]{2} \)

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\(\,\,\,\,\,\sqrt[3]{-250}\)

\(\,\,\,\,\,\sqrt[3]{-125\cdot2}\)

\(\,\,\,\,\,\sqrt[3]{-125}\cdot\sqrt[3]{2}\)

\(\,\,\,\,\,-5\sqrt[3]{2}\)

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

 

\(\textbf{20)}\) \( \sqrt[3]{x^6} \)

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The answer is \( x^2 \)

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\(\,\,\,\,\,\sqrt[3]{x^6}\)

\(\,\,\,\,\,\sqrt[3]{(x^2)^3}\)

\(\,\,\,\,\,x^2\)

\(\,\,\,\,\,\)The answer is \(x^2\)

 

See Related Pages\(\)

\(\bullet\text{ Multiplying Square Roots}\)
\(\,\,\,\,\,\,\,\, \sqrt{5} \cdot \sqrt{125} …\)

\(\bullet\text{ Dividing Square Roots}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{\sqrt{12}}{\sqrt{3}}…\)

\(\bullet\text{ Adding and Subtracting Square Roots}\)
\(\,\,\,\,\,\,\,\,3\sqrt{2}-7\sqrt{2}…\)