Simplifying cube roots means identifying perfect cube factors and pulling their cube roots outside the radical. Because cube roots are odd roots, negative numbers can have real cube roots, and variables do not require absolute value signs when a perfect cube is removed. The practice below includes perfect cubes, non-perfect cubes, negative values, and expressions containing variables.
Notes
Practice Problems
\(\textbf{1)}\) \(\sqrt[3]{16}\) 
The answer is \(2\sqrt[3]{2}\)
\(\,\,\,\,\,\sqrt[3]{16}\)
\(\,\,\,\,\,\sqrt[3]{8\cdot2}\)
\(\,\,\,\,\,\sqrt[3]{8}\cdot\sqrt[3]{2}\)
\(\,\,\,\,\,2\sqrt[3]{2}\)
The answer is \(2\sqrt[3]{2}\)
The answer is \(2\sqrt[3]{2}\)\(\,\,\,\,\,\sqrt[3]{16}\)
\(\,\,\,\,\,\sqrt[3]{8\cdot2}\)
\(\,\,\,\,\,\sqrt[3]{8}\cdot\sqrt[3]{2}\)
\(\,\,\,\,\,2\sqrt[3]{2}\)
The answer is \(2\sqrt[3]{2}\)
\(\textbf{2)}\) \(\sqrt[3]{-27}\) The answer is \(-3\)
\(\,\,\,\,\,\sqrt[3]{-27}\)
\(\,\,\,\,\,\sqrt[3]{(-3)(-3)(-3)}\)
\(\,\,\,\,\,-3\)
The answer is \(-3\)
The answer is \(-3\)\(\,\,\,\,\,\sqrt[3]{-27}\)
\(\,\,\,\,\,\sqrt[3]{(-3)(-3)(-3)}\)
\(\,\,\,\,\,-3\)
The answer is \(-3\)
\(\textbf{3)}\) \(\sqrt[3]{1000}\) The answer is \(10\)
\(\,\,\,\,\,\sqrt[3]{1000}\)
\(\,\,\,\,\,\sqrt[3]{10\cdot10\cdot10}\)
\(\,\,\,\,\,10\)
The answer is \(10\)
The answer is \(10\)\(\,\,\,\,\,\sqrt[3]{1000}\)
\(\,\,\,\,\,\sqrt[3]{10\cdot10\cdot10}\)
\(\,\,\,\,\,10\)
The answer is \(10\)
\(\textbf{4)}\) \(\sqrt[3]{54}\) The answer is \(3\sqrt[3]{2}\)
\(\,\,\,\,\,\sqrt[3]{54}\)
\(\,\,\,\,\,\sqrt[3]{27\cdot2}\)
\(\,\,\,\,\,\sqrt[3]{27}\cdot\sqrt[3]{2}\)
\(\,\,\,\,\,3\sqrt[3]{2}\)
The answer is \(3\sqrt[3]{2}\)
\(\,\,\,\,\,\sqrt[3]{54}\)
\(\,\,\,\,\,\sqrt[3]{27\cdot2}\)
\(\,\,\,\,\,\sqrt[3]{27}\cdot\sqrt[3]{2}\)
\(\,\,\,\,\,3\sqrt[3]{2}\)
The answer is \(3\sqrt[3]{2}\)
\(\textbf{5)}\) \(\sqrt[3]{-1}\) The answer is \(-1\)
\(\,\,\,\,\,\sqrt[3]{-1}\)
\(\,\,\,\,\,\sqrt[3]{(-1)(-1)(-1)}\)
\(\,\,\,\,\,-1\)
The answer is \(-1\)
\(\,\,\,\,\,\sqrt[3]{-1}\)
\(\,\,\,\,\,\sqrt[3]{(-1)(-1)(-1)}\)
\(\,\,\,\,\,-1\)
The answer is \(-1\)
\(\textbf{6)}\) \(\sqrt[3]{1}\) The answer is \(1\)
\(\,\,\,\,\,\sqrt[3]{1}\)
\(\,\,\,\,\,\sqrt[3]{1\cdot1\cdot1}\)
\(\,\,\,\,\,1\)
The answer is \(1\)
\(\,\,\,\,\,\sqrt[3]{1}\)
\(\,\,\,\,\,\sqrt[3]{1\cdot1\cdot1}\)
\(\,\,\,\,\,1\)
The answer is \(1\)
\(\textbf{7)}\) \(\sqrt[3]{-8}\) The answer is \(-2\)
\(\,\,\,\,\,\sqrt[3]{-8}\)
\(\,\,\,\,\,\sqrt[3]{(-2)(-2)(-2)}\)
\(\,\,\,\,\,-2\)
The answer is \(-2\)
\(\,\,\,\,\,\sqrt[3]{-8}\)
\(\,\,\,\,\,\sqrt[3]{(-2)(-2)(-2)}\)
\(\,\,\,\,\,-2\)
The answer is \(-2\)
\(\textbf{8)}\) \(\sqrt[3]{24a^2b^3c^5d^6}\) The answer is \(2bcd^2\sqrt[3]{3a^2c^2}\)
\(\,\,\,\,\,\sqrt[3]{24a^2b^3c^5d^6}\)
\(\,\,\,\,\,\sqrt[3]{8\cdot3\cdot a^2\cdot b^3\cdot c^3\cdot c^2\cdot d^6}\)
\(\,\,\,\,\,\sqrt[3]{8b^3c^3d^6}\sqrt[3]{3a^2c^2}\)
\(\,\,\,\,\,2bcd^2\sqrt[3]{3a^2c^2}\)
The answer is \(2bcd^2\sqrt[3]{3a^2c^2}\)
\(\,\,\,\,\,\sqrt[3]{24a^2b^3c^5d^6}\)
\(\,\,\,\,\,\sqrt[3]{8\cdot3\cdot a^2\cdot b^3\cdot c^3\cdot c^2\cdot d^6}\)
\(\,\,\,\,\,\sqrt[3]{8b^3c^3d^6}\sqrt[3]{3a^2c^2}\)
\(\,\,\,\,\,2bcd^2\sqrt[3]{3a^2c^2}\)
The answer is \(2bcd^2\sqrt[3]{3a^2c^2}\)
\(\textbf{9)}\) \(\sqrt[3]{-10x^2y^{10}z^3}\) The answer is \(-y^3z\sqrt[3]{10x^2y}\)
\(\,\,\,\,\,\sqrt[3]{-10x^2y^{10}z^3}\)
\(\,\,\,\,\,\sqrt[3]{-10x^2\cdot y^9\cdot y\cdot z^3}\)
\(\,\,\,\,\,\sqrt[3]{y^9z^3}\sqrt[3]{-10x^2y}\)
\(\,\,\,\,\,-y^3z\sqrt[3]{10x^2y}\)
The answer is \(-y^3z\sqrt[3]{10x^2y}\)
\(\,\,\,\,\,\sqrt[3]{-10x^2y^{10}z^3}\)
\(\,\,\,\,\,\sqrt[3]{-10x^2\cdot y^9\cdot y\cdot z^3}\)
\(\,\,\,\,\,\sqrt[3]{y^9z^3}\sqrt[3]{-10x^2y}\)
\(\,\,\,\,\,-y^3z\sqrt[3]{10x^2y}\)
The answer is \(-y^3z\sqrt[3]{10x^2y}\)
\(\textbf{10)}\) \(\sqrt[3]{-32xy^2z^9}\) The answer is \(-2z^3\sqrt[3]{4xy^2}\)
\(\,\,\,\,\,\sqrt[3]{-32xy^2z^9}\)
\(\,\,\,\,\,\sqrt[3]{-8\cdot4xy^2\cdot z^9}\)
\(\,\,\,\,\,\sqrt[3]{-8z^9}\sqrt[3]{4xy^2}\)
\(\,\,\,\,\,-2z^3\sqrt[3]{4xy^2}\)
The answer is \(-2z^3\sqrt[3]{4xy^2}\)
\(\,\,\,\,\,\sqrt[3]{-32xy^2z^9}\)
\(\,\,\,\,\,\sqrt[3]{-8\cdot4xy^2\cdot z^9}\)
\(\,\,\,\,\,\sqrt[3]{-8z^9}\sqrt[3]{4xy^2}\)
\(\,\,\,\,\,-2z^3\sqrt[3]{4xy^2}\)
The answer is \(-2z^3\sqrt[3]{4xy^2}\)
\(\textbf{11)}\) \(\sqrt[3]{-x^3}\) The answer is \(-x\)
\(\,\,\,\,\,\sqrt[3]{-x^3}\)
\(\,\,\,\,\,\sqrt[3]{(-1)^3x^3}\)
\(\,\,\,\,\,-x\)
The answer is \(-x\)
\(\,\,\,\,\,\sqrt[3]{-x^3}\)
\(\,\,\,\,\,\sqrt[3]{(-1)^3x^3}\)
\(\,\,\,\,\,-x\)
The answer is \(-x\)
\(\textbf{12)}\) \(\sqrt[3]{128}\) The answer is \(4\sqrt[3]{2}\)
\(\,\,\,\,\,\sqrt[3]{128}\)
\(\,\,\,\,\,\sqrt[3]{64\cdot2}\)
\(\,\,\,\,\,\sqrt[3]{64}\sqrt[3]{2}\)
\(\,\,\,\,\,4\sqrt[3]{2}\)
The answer is \(4\sqrt[3]{2}\)
\(\,\,\,\,\,\sqrt[3]{128}\)
\(\,\,\,\,\,\sqrt[3]{64\cdot2}\)
\(\,\,\,\,\,\sqrt[3]{64}\sqrt[3]{2}\)
\(\,\,\,\,\,4\sqrt[3]{2}\)
The answer is \(4\sqrt[3]{2}\)
\(\textbf{13)}\) \(\sqrt[3]{250}\) The answer is \(5\sqrt[3]{2}\)
\(\,\,\,\,\,\sqrt[3]{250}\)
\(\,\,\,\,\,\sqrt[3]{125\cdot2}\)
\(\,\,\,\,\,\sqrt[3]{125}\sqrt[3]{2}\)
\(\,\,\,\,\,5\sqrt[3]{2}\)
The answer is \(5\sqrt[3]{2}\)
\(\,\,\,\,\,\sqrt[3]{250}\)
\(\,\,\,\,\,\sqrt[3]{125\cdot2}\)
\(\,\,\,\,\,\sqrt[3]{125}\sqrt[3]{2}\)
\(\,\,\,\,\,5\sqrt[3]{2}\)
The answer is \(5\sqrt[3]{2}\)
\(\textbf{14)}\) \(\sqrt[3]{-432}\) The answer is \(-6\sqrt[3]{2}\)
\(\,\,\,\,\,\sqrt[3]{-432}\)
\(\,\,\,\,\,\sqrt[3]{-216\cdot2}\)
\(\,\,\,\,\,\sqrt[3]{-216}\sqrt[3]{2}\)
\(\,\,\,\,\,-6\sqrt[3]{2}\)
The answer is \(-6\sqrt[3]{2}\)
\(\,\,\,\,\,\sqrt[3]{-432}\)
\(\,\,\,\,\,\sqrt[3]{-216\cdot2}\)
\(\,\,\,\,\,\sqrt[3]{-216}\sqrt[3]{2}\)
\(\,\,\,\,\,-6\sqrt[3]{2}\)
The answer is \(-6\sqrt[3]{2}\)
\(\textbf{15)}\) \(\sqrt[3]{81x^4}\) The answer is \(3x\sqrt[3]{3x}\)
\(\,\,\,\,\,\sqrt[3]{81x^4}\)
\(\,\,\,\,\,\sqrt[3]{27\cdot3\cdot x^3\cdot x}\)
\(\,\,\,\,\,\sqrt[3]{27x^3}\sqrt[3]{3x}\)
\(\,\,\,\,\,3x\sqrt[3]{3x}\)
The answer is \(3x\sqrt[3]{3x}\)
\(\,\,\,\,\,\sqrt[3]{81x^4}\)
\(\,\,\,\,\,\sqrt[3]{27\cdot3\cdot x^3\cdot x}\)
\(\,\,\,\,\,\sqrt[3]{27x^3}\sqrt[3]{3x}\)
\(\,\,\,\,\,3x\sqrt[3]{3x}\)
The answer is \(3x\sqrt[3]{3x}\)
\(\textbf{16)}\) \(\sqrt[3]{16a^7b^4}\) The answer is \(2a^2b\sqrt[3]{2ab}\)
\(\,\,\,\,\,\sqrt[3]{16a^7b^4}\)
\(\,\,\,\,\,\sqrt[3]{8\cdot2\cdot a^6\cdot a\cdot b^3\cdot b}\)
\(\,\,\,\,\,\sqrt[3]{8a^6b^3}\sqrt[3]{2ab}\)
\(\,\,\,\,\,2a^2b\sqrt[3]{2ab}\)
The answer is \(2a^2b\sqrt[3]{2ab}\)
\(\,\,\,\,\,\sqrt[3]{16a^7b^4}\)
\(\,\,\,\,\,\sqrt[3]{8\cdot2\cdot a^6\cdot a\cdot b^3\cdot b}\)
\(\,\,\,\,\,\sqrt[3]{8a^6b^3}\sqrt[3]{2ab}\)
\(\,\,\,\,\,2a^2b\sqrt[3]{2ab}\)
The answer is \(2a^2b\sqrt[3]{2ab}\)
\(\textbf{17)}\) \(\sqrt[3]{-54m^5n^6}\) The answer is \(-3mn^2\sqrt[3]{2m^2}\)
\(\,\,\,\,\,\sqrt[3]{-54m^5n^6}\)
\(\,\,\,\,\,\sqrt[3]{-27\cdot2\cdot m^3\cdot m^2\cdot n^6}\)
\(\,\,\,\,\,\sqrt[3]{-27m^3n^6}\sqrt[3]{2m^2}\)
\(\,\,\,\,\,-3mn^2\sqrt[3]{2m^2}\)
The answer is \(-3mn^2\sqrt[3]{2m^2}\)
\(\,\,\,\,\,\sqrt[3]{-54m^5n^6}\)
\(\,\,\,\,\,\sqrt[3]{-27\cdot2\cdot m^3\cdot m^2\cdot n^6}\)
\(\,\,\,\,\,\sqrt[3]{-27m^3n^6}\sqrt[3]{2m^2}\)
\(\,\,\,\,\,-3mn^2\sqrt[3]{2m^2}\)
The answer is \(-3mn^2\sqrt[3]{2m^2}\)
\(\textbf{18)}\) \(\sqrt[3]{375p^3q^8}\) The answer is \(5pq^2\sqrt[3]{3q^2}\)
\(\,\,\,\,\,\sqrt[3]{375p^3q^8}\)
\(\,\,\,\,\,\sqrt[3]{125\cdot3\cdot p^3\cdot q^6\cdot q^2}\)
\(\,\,\,\,\,\sqrt[3]{125p^3q^6}\sqrt[3]{3q^2}\)
\(\,\,\,\,\,5pq^2\sqrt[3]{3q^2}\)
The answer is \(5pq^2\sqrt[3]{3q^2}\)
\(\,\,\,\,\,\sqrt[3]{375p^3q^8}\)
\(\,\,\,\,\,\sqrt[3]{125\cdot3\cdot p^3\cdot q^6\cdot q^2}\)
\(\,\,\,\,\,\sqrt[3]{125p^3q^6}\sqrt[3]{3q^2}\)
\(\,\,\,\,\,5pq^2\sqrt[3]{3q^2}\)
The answer is \(5pq^2\sqrt[3]{3q^2}\)
\(\textbf{19)}\) \(\sqrt[3]{216x^9y^3}\) The answer is \(6x^3y\)
\(\,\,\,\,\,\sqrt[3]{216x^9y^3}\)
\(\,\,\,\,\,\sqrt[3]{6^3(x^3)^3y^3}\)
\(\,\,\,\,\,6x^3y\)
The answer is \(6x^3y\)
\(\,\,\,\,\,\sqrt[3]{216x^9y^3}\)
\(\,\,\,\,\,\sqrt[3]{6^3(x^3)^3y^3}\)
\(\,\,\,\,\,6x^3y\)
The answer is \(6x^3y\)
\(\textbf{20)}\) \(\sqrt[3]{-686a^4b^7}\) The answer is \(-7ab^2\sqrt[3]{2ab}\)
\(\,\,\,\,\,\sqrt[3]{-686a^4b^7}\)
\(\,\,\,\,\,\sqrt[3]{-343\cdot2\cdot a^3\cdot a\cdot b^6\cdot b}\)
\(\,\,\,\,\,\sqrt[3]{-343a^3b^6}\sqrt[3]{2ab}\)
\(\,\,\,\,\,-7ab^2\sqrt[3]{2ab}\)
The answer is \(-7ab^2\sqrt[3]{2ab}\)
\(\,\,\,\,\,\sqrt[3]{-686a^4b^7}\)
\(\,\,\,\,\,\sqrt[3]{-343\cdot2\cdot a^3\cdot a\cdot b^6\cdot b}\)
\(\,\,\,\,\,\sqrt[3]{-343a^3b^6}\sqrt[3]{2ab}\)
\(\,\,\,\,\,-7ab^2\sqrt[3]{2ab}\)
The answer is \(-7ab^2\sqrt[3]{2ab}\)
Related Pages
\(\bullet\text{ Square Roots}\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\sqrt{72}…\)