Cube - Simplifying from Factors, Values and Variables, Radical Remaining (Level 2)

This math topic focuses on simplifying cube radicals involving numerical factors, values, and variables, while handling any remaining radicals in the expression. Each problem presents a radical containing combinations of prime and composite numbers multiplied by variable factors. The students are tasked with simplifying these expressions to their simplest form, showcasing a fundamental understanding of radical simplification techniques—especially pertaining to dealing with cube roots in algebra. This skill set is crucial for algebraic manipulation and problem-solving in more advanced math courses.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Radicals - Cube - Simplifying from Factors, Values and Variables, Radical Remaining Worksheet

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Radicals - Cube - Simplifying from Factors, Values and Variables, Radical Remaining
1
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 3 times z times z times z times z
a A LaTex expression showing zsquare root of 5
b A LaTex expression showing {z} to the power of 3 square root of 2
c A LaTex expression showing 2{z} to the power of 2 square root of 3
d A LaTex expression showing 3{z} to the power of 4 square root of 4
e A LaTex expression showing 4{z} to the power of 4 square root of 6
2
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times 2 times 3 times x times x
a A LaTex expression showing {x} to the power of 3
b A LaTex expression showing 4xsquare root of 3
c A LaTex expression showing {x} to the power of 2 square root of 3
d A LaTex expression showing {x} to the power of 3 square root of 4
e A LaTex expression showing xsquare root of 5
3
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 11 times m times m
a A LaTex expression showing 2msquare root of 8
b A LaTex expression showing msquare root of 10
c A LaTex expression showing 2msquare root of 11
d A LaTex expression showing 4msquare root of 10
e A LaTex expression showing 3msquare root of 14
4
Simplify the radical
A LaTex expression showing square root of 2 times 3 times 3 times r
a A LaTex expression showing 6square root of 5{r to the power of 2 }
b A LaTex expression showing 3square root of 2r
c A LaTex expression showing square root of 2r
d A LaTex expression showing square root of 5{r to the power of 3 }
e A LaTex expression showing 2square root of 5r
5
Simplify the radical
A LaTex expression showing square root of 5 times 5 times 7 times d times d times d times d times d
a A LaTex expression showing 7{d} to the power of 4 square root of 3{d to the power of 2 }
b A LaTex expression showing {d} to the power of 3 square root of 4{d to the power of 3 }
c A LaTex expression showing 5{d} to the power of 2 square root of 7d
d A LaTex expression showing {d} to the power of 2 square root of 4d
e A LaTex expression showing 6{d} to the power of 4 square root of 4d
6
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times 2 times 2 times n
a A LaTex expression showing 4square root of 2n
b A LaTex expression showing 5square root of n
c A LaTex expression showing 4square root of {n to the power of 3 }
d A LaTex expression showing 3square root of {n to the power of 2 }
7
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times 2 times 7 times c times c times c times c times c
a A LaTex expression showing {c} to the power of 2 square root of 5c
b A LaTex expression showing {c} to the power of 3 square root of 8c
c A LaTex expression showing 4{c} to the power of 2 square root of 5{c to the power of 3 }
d A LaTex expression showing 5{c} to the power of 4 square root of 8{c to the power of 2 }
e A LaTex expression showing 4{c} to the power of 2 square root of 7c
8
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times 2 times 2 times c times c times c times c times c
a A LaTex expression showing 5csquare root of c
b A LaTex expression showing 5{c} to the power of 2 square root of {c to the power of 3 }
c A LaTex expression showing 4{c} to the power of 2 square root of 2c
d A LaTex expression showing 7{c} to the power of 2 square root of c
e A LaTex expression showing csquare root of 2c