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Radicals - 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

2â‹…2â‹…2â‹…2â‹…mâ‹…mâ‹…pâ‹…pâ‹…pâ‹…p\sqrt{2\cdot 2\cdot 2\cdot 2\cdot m\cdot m\cdot p\cdot p\cdot p\cdot p}

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 2 times 2 times x times x times x times x times y times y
a A LaTex expression showing {x} to the power of 2 ysquare root of 2
b A LaTex expression showing x{y} to the power of 2 square root of 2
c A LaTex expression showing 4{x} to the power of 3 y
d A LaTex expression showing {x} to the power of 2 {y} to the power of 3
e A LaTex expression showing 2{x} to the power of 2 y
f A LaTex expression showing 3x{y} to the power of 3
2
Simplify the radical
A LaTex expression showing square root of 2 times 2 times n times n times p times p
a A LaTex expression showing 2n{p} to the power of 2 square root of 3
b A LaTex expression showing 2np
c A LaTex expression showing n{p} to the power of 3
d A LaTex expression showing 4np
e A LaTex expression showing 4n{p} to the power of 2
f A LaTex expression showing 5n{p} to the power of 3 square root of 4
3
Simplify the radical
A LaTex expression showing square root of 3 times 3 times d times d times y times y times y times y
a A LaTex expression showing 4d{y} to the power of 4 square root of 3
b A LaTex expression showing 6{d} to the power of 2 {y} to the power of 4 square root of 4
c A LaTex expression showing 3d{y} to the power of 2
d A LaTex expression showing 4d{y} to the power of 4
e A LaTex expression showing {d} to the power of 3 y
f A LaTex expression showing 3d{y} to the power of 4 square root of 4
4
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 2zysquare root of 2
c A LaTex expression showing 4z{y} to the power of 2 square root of 3
d A LaTex expression showing 7{z} to the power of 2 y
e A LaTex expression showing z{y} to the power of 2
f A LaTex expression showing 5zy
5
Simplify the radical
A LaTex expression showing square root of 5 times 5 times d times d times z times z
a A LaTex expression showing 4d{z} to the power of 3 square root of 4
b A LaTex expression showing 5{d} to the power of 2 z
c A LaTex expression showing 7dz
d A LaTex expression showing dz
e A LaTex expression showing 5dz
f A LaTex expression showing 3dz
6
Simplify the radical
A LaTex expression showing square root of 3 times 3 times n times n times n times n times p times p
a A LaTex expression showing 3n{p} to the power of 2
b A LaTex expression showing 6{n} to the power of 4 p
c A LaTex expression showing 2n{p} to the power of 2
d A LaTex expression showing npsquare root of 4
e A LaTex expression showing 3{n} to the power of 2 p
f A LaTex expression showing {n} to the power of 2 p
7
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times 2 times r times r times b times b
a A LaTex expression showing {r} to the power of 2 {b} to the power of 2 square root of 4
b A LaTex expression showing 3{r} to the power of 3 b
c A LaTex expression showing 7rbsquare root of 3
d A LaTex expression showing r{b} to the power of 3 square root of 3
e A LaTex expression showing 6r{b} to the power of 3
f A LaTex expression showing 4rb