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

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Simplify the radical

3311nnn\sqrt{3\cdot 3\cdot 11\cdot n\cdot n\cdot n}

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

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Math worksheet on 'Radicals - Cube - Simplifying from Factors, Values and Variables, Radical Remaining (Level 2)'. Part of a broader unit on 'Radicals - Simplifying Practice' Learn online: app.mobius.academy/math/units/radicals_simplifying_practice/
1
Simplify the radical
A LaTex expression showing square root of 5 times 5 times 5 times c times c times c times c
a A LaTex expression showing 8csquare root of 7
b A LaTex expression showing 5{c} to the power of 4
c A LaTex expression showing {c} to the power of 2
d A LaTex expression showing 6{c} to the power of 2 square root of 5
e A LaTex expression showing 5{c} to the power of 2 square root of 5
f A LaTex expression showing 6{c} to the power of 2 square root of 6
2
Simplify the radical
A LaTex expression showing square root of 3 times 3 times 7 times d times d times d times d
a A LaTex expression showing 2dsquare root of 9
b A LaTex expression showing 6{d} to the power of 4 square root of 8
c A LaTex expression showing 3{d} to the power of 2 square root of 7
d A LaTex expression showing 3dsquare root of 8
e A LaTex expression showing 5{d} to the power of 2 square root of 3
f A LaTex expression showing 6{d} to the power of 2 square root of 7
3
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 11 times n times n times n
a A LaTex expression showing 2{n} to the power of 3 square root of 9{n to the power of 2 }
b A LaTex expression showing nsquare root of 14{n to the power of 2 }
c A LaTex expression showing {n} to the power of 2 square root of 13{n to the power of 3 }
d A LaTex expression showing 2nsquare root of 11n
e A LaTex expression showing 3{n} to the power of 2 square root of 10{n to the power of 2 }
f A LaTex expression showing {n} to the power of 3 square root of 7n
4
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times z
a A LaTex expression showing square root of 3{z to the power of 2 }
b A LaTex expression showing 5square root of 3{z to the power of 2 }
c A LaTex expression showing square root of 3z
d A LaTex expression showing 2square root of 2z
e A LaTex expression showing square root of z
f A LaTex expression showing 4square root of 4z
5
Simplify the radical
A LaTex expression showing square root of 5 times 5 times 5 times d times d times d times d
a A LaTex expression showing 6{d} to the power of 4 square root of 5
b A LaTex expression showing 3dsquare root of 8
c A LaTex expression showing {d} to the power of 2
d A LaTex expression showing 3d
e A LaTex expression showing 5dsquare root of 6
f A LaTex expression showing 5{d} to the power of 2 square root of 5
6
Simplify the radical
A LaTex expression showing square root of 3 times 3 times 11 times n times n times n
a A LaTex expression showing 3nsquare root of 11n
b A LaTex expression showing 4nsquare root of 11n
c A LaTex expression showing {n} to the power of 2 square root of 8n
d A LaTex expression showing {n} to the power of 2 square root of 11n
e A LaTex expression showing 3{n} to the power of 3 square root of 9n
f A LaTex expression showing 6{n} to the power of 2 square root of 13{n to the power of 3 }
7
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 11 times z times z
a A LaTex expression showing 4zsquare root of 10
b A LaTex expression showing 2zsquare root of 11
c A LaTex expression showing {z} to the power of 3 square root of 9
d A LaTex expression showing zsquare root of 13
e A LaTex expression showing zsquare root of 10
f A LaTex expression showing 2{z} to the power of 2 square root of 10