Cube - Simplifying from Factors, Values and Variables, Nothing Remaining (Level 3)

This math topic focuses on simplifying cube radicals with various factors, values, and variables, without anything remaining. As part of an advanced simplifying radicals unit, it requires students to manipulate expressions involving mixed multiplication of numerical coefficients and variable bases raised to powers under cube root radicals. The problems include multiple-choice answers, each illustrating different simplified forms, helping learners enhance their competency in handling cube roots algebraically while applying foundational algebra rules and radical properties.

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, Nothing Remaining

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Simplify the radical

22ddddbb\sqrt{2\cdot 2\cdot d\cdot d\cdot d\cdot d\cdot b\cdot b}

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Radicals - Cube - Simplifying from Factors, Values and Variables, Nothing Remaining Worksheet

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Math worksheet on 'Radicals - Cube - Simplifying from Factors, Values and Variables, Nothing Remaining (Level 3)'. Part of a broader unit on 'Radicals - Simplifying Advanced' Learn online: app.mobius.academy/math/units/radicals_simplifying_advanced/
1
Simplify the radical
A LaTex expression showing square root of 3 times 3 times n times n times c times c
a A LaTex expression showing 2{n} to the power of 2 csquare root of 3
b A LaTex expression showing 6{n} to the power of 3 c
c A LaTex expression showing n{c} to the power of 2 square root of 4
d A LaTex expression showing 5{n} to the power of 3 {c} to the power of 3
e A LaTex expression showing 3nc
f A LaTex expression showing 3{n} to the power of 2 csquare root of 4
2
Simplify the radical
A LaTex expression showing square root of 2 times 2 times b times b times b times b times d times d times d times d
a A LaTex expression showing b{d} to the power of 2
b A LaTex expression showing 5{b} to the power of 4 d
c A LaTex expression showing 2{b} to the power of 2 {d} to the power of 2
d A LaTex expression showing 5b{d} to the power of 4
e A LaTex expression showing b{d} to the power of 4
f A LaTex expression showing {b} to the power of 2 {d} to the power of 3 square root of 2
3
A LaTex expression showing square root of 2 times 2 times 2 times 2 times m times m times p times p times p times p
Simplify the radical
a A LaTex expression showing 4m{p} to the power of 4
b A LaTex expression showing 7mp
c A LaTex expression showing {m} to the power of 2 psquare root of 2
d A LaTex expression showing m{p} to the power of 4
e A LaTex expression showing 4m{p} to the power of 2
f A LaTex expression showing 4{m} to the power of 3 {p} to the power of 2
4
Simplify the radical
A LaTex expression showing square root of 2 times 2 times p times p times z times z times z times z
a A LaTex expression showing {p} to the power of 3 z
b A LaTex expression showing 3{p} to the power of 3 {z} to the power of 3
c A LaTex expression showing 2pz
d A LaTex expression showing 2p{z} to the power of 2
e A LaTex expression showing 5{p} to the power of 3 {z} to the power of 4
f A LaTex expression showing pz
5
Simplify the radical
A LaTex expression showing square root of 5 times 5 times x times x times x times x times z times z
a A LaTex expression showing 3{x} to the power of 3 zsquare root of 4
b A LaTex expression showing 6x{z} to the power of 2 square root of 3
c A LaTex expression showing 4{x} to the power of 4 z
d A LaTex expression showing {x} to the power of 2 {z} to the power of 3 square root of 4
e A LaTex expression showing 5{x} to the power of 2 z
f A LaTex expression showing 8{x} to the power of 3 z
6
Simplify the radical
A LaTex expression showing square root of 5 times 5 times z times z times y times y
a A LaTex expression showing 3{z} to the power of 3 {y} to the power of 3
b A LaTex expression showing 7{z} to the power of 2 y
c A LaTex expression showing 4z{y} to the power of 2 square root of 3
d A LaTex expression showing 2zysquare root of 2
e A LaTex expression showing 5zy
f A LaTex expression showing z{y} to the power of 2
7
Simplify the radical
A LaTex expression showing square root of 2 times 2 times p times p times r times r
a A LaTex expression showing 5{p} to the power of 3 r
b A LaTex expression showing {p} to the power of 2 rsquare root of 2
c A LaTex expression showing 4pr
d A LaTex expression showing p{r} to the power of 3
e A LaTex expression showing 2pr
f A LaTex expression showing prsquare root of 3