Lesson
Practice Problems
Simplify
\(\textbf{1)}\) \( \sqrt[3]{48} \)
The answer is \( 2\sqrt[3]{6} \)
\(\,\,\,\,\,\sqrt[3]{48}\)
\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2\cdot2\cdot3}\)
\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2}\cdot\sqrt[3]{2\cdot3}\)
\(\,\,\,\,\,\sqrt[3]{8}\cdot\sqrt[3]{6}\)
\(\,\,\,\,\,2\sqrt[3]{6}\)
\(\textbf{2)}\) \( \sqrt[3]{24} \)
The answer is \( 2\sqrt[3]{3} \)
\(\,\,\,\,\,\sqrt[3]{24}\)
\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2\cdot3}\)
\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2}\cdot\sqrt[3]{3}\)
\(\,\,\,\,\,\sqrt[3]{8}\cdot\sqrt[3]{3}\)
\(\,\,\,\,\,2\sqrt[3]{3}\)
\(\textbf{3)}\) \( \sqrt[3]{240} \)
The answer is \( 2\sqrt[3]{30} \)
\(\,\,\,\,\,\sqrt[3]{240}\)
\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2\cdot2\cdot3\cdot5}\)
\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2}\cdot\sqrt[3]{2\cdot3\cdot5}\)
\(\,\,\,\,\,\sqrt[3]{8}\cdot\sqrt[3]{30}\)
\(\,\,\,\,\,2\sqrt[3]{30}\)
\(\textbf{4)}\) \( \sqrt[3]{128} \)
The answer is \( 4\sqrt[3]{2} \)
\(\,\,\,\,\,\sqrt[3]{128}\)
\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2}\)
\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2\cdot2\cdot2\cdot2}\cdot\sqrt[3]{2}\)
\(\,\,\,\,\,\sqrt[3]{64}\cdot\sqrt[3]{2}\)
\(\,\,\,\,\,4\sqrt[3]{2}\)
\(\textbf{5)}\) \( \sqrt[3]{135} \)
The answer is \( 3\sqrt[3]{5} \)
\(\,\,\,\,\,\sqrt[3]{135}\)
\(\,\,\,\,\,\sqrt[3]{3\cdot3\cdot3\cdot5}\)
\(\,\,\,\,\,\sqrt[3]{3\cdot3\cdot3}\cdot\sqrt[3]{5}\)
\(\,\,\,\,\,\sqrt[3]{27}\cdot\sqrt[3]{5}\)
\(\,\,\,\,\,3\sqrt[3]{5}\)
\(\textbf{6)}\) \( \sqrt[3]{2160} \)
The answer is \( 6\sqrt[3]{10} \)
\(\,\,\,\,\,\sqrt[3]{2160}\)
\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot5}\)
\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2}\cdot\sqrt[3]{3\cdot3\cdot3}\cdot\sqrt[3]{2\cdot5}\)
\(\,\,\,\,\,\sqrt[3]{8}\cdot\sqrt[3]{27}\cdot\sqrt[3]{5}\)
\(\,\,\,\,\,2\cdot3\sqrt[3]{5}\)
\(\,\,\,\,\,6\sqrt[3]{5}\)
\(\textbf{7)}\) \( \sqrt[3]{375} \)
The answer is \( 5\sqrt[3]{3} \)
\(\,\,\,\,\,\sqrt[3]{375}\)
\(\,\,\,\,\,\sqrt[3]{3\cdot5\cdot5\cdot5}\)
\(\,\,\,\,\,\sqrt[3]{3}\cdot\sqrt[3]{5\cdot5\cdot5}\)
\(\,\,\,\,\,\sqrt[3]{3}\cdot\sqrt[3]{125}\)
\(\,\,\,\,\,5\sqrt[3]{3}\)
\(\textbf{8)}\) \( \sqrt[3]{960} \)
The answer is \( 4\sqrt[3]{15} \)
\(\,\,\,\,\,\sqrt[3]{960}\)
\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5}\)
\(\,\,\,\,\,\sqrt[3]{2\cdot2\cdot2\cdot2\cdot2\cdot2}\cdot\sqrt[3]{3\cdot5}\)
\(\,\,\,\,\,\sqrt[3]{64}\cdot\sqrt[3]{15}\)
\(\,\,\,\,\,4\sqrt[3]{15}\)
\(\textbf{9)}\) \( \sqrt[3]{686} \)
The answer is \( 7\sqrt[3]{2} \)
\(\,\,\,\,\,\sqrt[3]{686}\)
\(\,\,\,\,\,\sqrt[3]{2\cdot7\cdot7\cdot7}\)
\(\,\,\,\,\,\sqrt[3]{2}\cdot\sqrt[3]{7\cdot7\cdot7}\)
\(\,\,\,\,\,\sqrt[3]{2}\cdot\sqrt[3]{343}\)
\(\,\,\,\,\,7\sqrt[3]{2}\)
