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

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Radicals - Cube - Simplifying from Factors, Values and Variables, Nothing Remaining
1
Simplify the radical
A LaTex expression showing square root of 2 times 2 times d times d times b times b
a A LaTex expression showing 3dbsquare root of 4
b A LaTex expression showing db
c A LaTex expression showing 5d{b} to the power of 2 square root of 2
d A LaTex expression showing {d} to the power of 3 bsquare root of 2
e A LaTex expression showing 2db
2
Simplify the radical
A LaTex expression showing square root of 5 times 5 times p times p times p times p times y times y times y times y
a A LaTex expression showing 7{p} to the power of 4 {y} to the power of 3
b A LaTex expression showing 4{p} to the power of 4 ysquare root of 3
c A LaTex expression showing 5{p} to the power of 2 {y} to the power of 2
d A LaTex expression showing 2{p} to the power of 4 {y} to the power of 4 square root of 2
e A LaTex expression showing 3{p} to the power of 4 {y} to the power of 2
3
Simplify the radical
A LaTex expression showing square root of 3 times 3 times p times p times p times p times d times d
a A LaTex expression showing 6{p} to the power of 3 d
b A LaTex expression showing 3{p} to the power of 2 d
c A LaTex expression showing 5{p} to the power of 4 d
d A LaTex expression showing 5pdsquare root of 3
e A LaTex expression showing {p} to the power of 3 d
4
Simplify the radical
A LaTex expression showing square root of 5 times 5 times n times n times y times y times y times y
a A LaTex expression showing 6{n} to the power of 3 y
b A LaTex expression showing 2nysquare root of 2
c A LaTex expression showing ny
d A LaTex expression showing 5n{y} to the power of 2
e A LaTex expression showing 4{n} to the power of 3 {y} to the power of 3
5
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times 2 times p times p times n times n
a A LaTex expression showing 3{p} to the power of 3 {n} to the power of 3
b A LaTex expression showing 4pn
c A LaTex expression showing 3{p} to the power of 3 {n} to the power of 2 square root of 2
d A LaTex expression showing {p} to the power of 2 {n} to the power of 3
e A LaTex expression showing 4{p} to the power of 2 {n} to the power of 2 square root of 3
6
Simplify the radical
A LaTex expression showing square root of 2 times 2 times n times n times m times m times m times m
a A LaTex expression showing 2n{m} to the power of 2
b A LaTex expression showing 5{n} to the power of 3 {m} to the power of 3
c A LaTex expression showing n{m} to the power of 3
d A LaTex expression showing 3{n} to the power of 3 {m} to the power of 3
e A LaTex expression showing nm
7
Simplify the radical
A LaTex expression showing square root of 5 times 5 times n times n times z times z times z times z
a A LaTex expression showing 8n{z} to the power of 2
b A LaTex expression showing 7n{z} to the power of 2 square root of 4
c A LaTex expression showing 8{n} to the power of 3 {z} to the power of 4
d A LaTex expression showing {n} to the power of 3 zsquare root of 2
e A LaTex expression showing 5n{z} to the power of 2
8
Simplify the radical
A LaTex expression showing square root of 5 times 5 times m times m times y times y
a A LaTex expression showing 8{m} to the power of 2 ysquare root of 3
b A LaTex expression showing 7m{y} to the power of 2 square root of 2
c A LaTex expression showing 5my
d A LaTex expression showing 6{m} to the power of 2 y
e A LaTex expression showing 3mysquare root of 3