Cube - Simplify From Cubed Factors, Values and Variables, Nothing Remaining (Level 3)

This math topic focuses on simplifying cube radicals with various cubed factors, constants, and variables, ensuring that no factors remain inside the radical upon simplification. The problems escalate in complexity and teach students to simplify expressions featuring powers and coefficients, helping them understand and manipulate radical terms effectively. Each question provides multiple-choice answers, allowing students to practice and confirm their understanding of the procedures involved in radical simplification at an advanced level.

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

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Radicals - Cube - Simplify From Cubed Factors, Values and Variables, Nothing Remaining Worksheet

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Radicals - Cube - Simplify From Cubed Factors, Values and Variables, Nothing Remaining
1
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times y to the power of 2 times y to the power of 2 times r to the power of 2 times r to the power of 2 times
a A LaTex expression showing 8{y} to the power of 2 {r} to the power of 3 square root of 3
b A LaTex expression showing 5{y} to the power of 2 {r} to the power of 2
c A LaTex expression showing 2yr
d A LaTex expression showing 6{y} to the power of 2 {r} to the power of 2
e A LaTex expression showing y{r} to the power of 3 square root of 3
2
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times r to the power of 2 times r to the power of 2 times y to the power of 2 times y to the power of 2 times
a A LaTex expression showing 2{r} to the power of 3 {y} to the power of 4 square root of 3
b A LaTex expression showing 5{r} to the power of 2 {y} to the power of 2
c A LaTex expression showing 3ry
d A LaTex expression showing 5{r} to the power of 4 y
e A LaTex expression showing 3r{y} to the power of 2
3
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times n to the power of 2 times n to the power of 2 times y to the power of 2 times
a A LaTex expression showing 5nysquare root of 2
b A LaTex expression showing 4{n} to the power of 2 {y} to the power of 3 square root of 3
c A LaTex expression showing {n} to the power of 4 {y} to the power of 2
d A LaTex expression showing 4ny
e A LaTex expression showing 2{n} to the power of 2 y
4
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times p to the power of 2 times p to the power of 2 times r to the power of 2 times
a A LaTex expression showing {p} to the power of 3 {r} to the power of 2 square root of 4
b A LaTex expression showing 6{p} to the power of 2 {r} to the power of 2
c A LaTex expression showing 5{p} to the power of 2 r
d A LaTex expression showing pr
e A LaTex expression showing 4prsquare root of 4
5
Simplify the radical
A LaTex expression showing square root of 3 to the power of 2 times n to the power of 2 times y to the power of 2 times y to the power of 2 times
a A LaTex expression showing 3n{y} to the power of 2
b A LaTex expression showing 3ny
c A LaTex expression showing 6n{y} to the power of 4 square root of 2
d A LaTex expression showing nysquare root of 3
e A LaTex expression showing 6n{y} to the power of 3 square root of 4
6
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times x to the power of 2 times x to the power of 2 times p to the power of 2 times p to the power of 2 times
a A LaTex expression showing 6{x} to the power of 2 p
b A LaTex expression showing 6{x} to the power of 3 {p} to the power of 2
c A LaTex expression showing {x} to the power of 3 {p} to the power of 3
d A LaTex expression showing 4x{p} to the power of 4
e A LaTex expression showing 5{x} to the power of 2 {p} to the power of 2
7
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times m to the power of 2 times m to the power of 2 times r to the power of 2 times r to the power of 2 times
a A LaTex expression showing 8{m} to the power of 4 rsquare root of 2
b A LaTex expression showing 5{m} to the power of 2 {r} to the power of 2
c A LaTex expression showing 5{m} to the power of 2 {r} to the power of 4
d A LaTex expression showing 8{m} to the power of 3 r
e A LaTex expression showing 5{m} to the power of 2 rsquare root of 4
8
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times r to the power of 2 times r to the power of 2 times n to the power of 2 times n to the power of 2 times
a A LaTex expression showing 3{r} to the power of 2 nsquare root of 3
b A LaTex expression showing 5{r} to the power of 2 {n} to the power of 2
c A LaTex expression showing 5{r} to the power of 3 {n} to the power of 2
d A LaTex expression showing {r} to the power of 4 n
e A LaTex expression showing 6{r} to the power of 3 n