Cube - Simplifying, Values and Variables, Radical Remaining (Level 3)

This math topic focuses on advanced radical simplification. It covers simplifying cube root expressions that involve both numerical and variable components. The problems challenge learners to simplify cube roots containing various powers of variables and coefficients, pushing students to separate terms that can be completely cubed from those that cannot, thus leaving a radical remaining. Each question presents multiple-choice answers for the students to select from after simplifying the given expressions. These skills are crucial for understanding higher-level algebra and preparing for topics in calculus and beyond.

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

more
View

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

Mobius Math Academy logo
Math worksheet on 'Radicals - Cube - Simplifying, Values and Variables, Radical 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 44{r to the power of 4 c}
a A LaTex expression showing rsquare root of 14{c to the power of 2 }
b A LaTex expression showing 2{r} to the power of 2 square root of 11c
c A LaTex expression showing rsquare root of 13c
d A LaTex expression showing rsquare root of 12c
e A LaTex expression showing 2rsquare root of 13c
2
Simplify the radical
A LaTex expression showing square root of 12p{b to the power of 2 }
a A LaTex expression showing 3bsquare root of p
b A LaTex expression showing {b} to the power of 2 square root of 2{p to the power of 3 }
c A LaTex expression showing 2bsquare root of 3p
d A LaTex expression showing 5bsquare root of 4p
3
Simplify the radical
A LaTex expression showing square root of 20{m to the power of 2 {y} to the power of 3 }
a A LaTex expression showing mysquare root of 5{y to the power of 3 }
b A LaTex expression showing mysquare root of 7{y to the power of 2 }
c A LaTex expression showing 2mysquare root of 5y
d A LaTex expression showing mysquare root of 8y
e A LaTex expression showing {m} to the power of 3 {y} to the power of 3 square root of 3y
4
Simplify the radical
A LaTex expression showing square root of 99{m to the power of 4 {r} to the power of 3 }
a A LaTex expression showing {m} to the power of 2 rsquare root of 14r
b A LaTex expression showing 3{m} to the power of 2 rsquare root of 11r
c A LaTex expression showing 3m{r} to the power of 3 square root of 7r
d A LaTex expression showing mrsquare root of 14{r to the power of 3 }
e A LaTex expression showing mrsquare root of 8r
5
Simplify the radical
A LaTex expression showing square root of 175{p to the power of 3 {r} to the power of 5 }
a A LaTex expression showing 5p{r} to the power of 2 square root of 7pr
b A LaTex expression showing prsquare root of 3pr
c A LaTex expression showing 2p{r} to the power of 2 square root of 9p{r to the power of 2 }
d A LaTex expression showing 7{p} to the power of 2 rsquare root of 6pr
e A LaTex expression showing 6{p} to the power of 3 {r} to the power of 2 square root of 5pr
6
Simplify the radical
A LaTex expression showing square root of 44{n to the power of 4 y}
a A LaTex expression showing {n} to the power of 3 square root of 7{y to the power of 2 }
b A LaTex expression showing nsquare root of 9y
c A LaTex expression showing 5{n} to the power of 2 square root of 11y
d A LaTex expression showing 4{n} to the power of 3 square root of 8y
e A LaTex expression showing 2{n} to the power of 2 square root of 11y
7
Simplify the radical
A LaTex expression showing square root of 112{d to the power of 4 r}
a A LaTex expression showing {d} to the power of 4 square root of 5{r to the power of 3 }
b A LaTex expression showing 7{d} to the power of 2 square root of 6r
c A LaTex expression showing {d} to the power of 3 square root of 7{r to the power of 2 }
d A LaTex expression showing 7{d} to the power of 4 square root of 7r
e A LaTex expression showing 4{d} to the power of 2 square root of 7r