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.

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

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Radicals - Cube - Simplifying, Values and Variables, Radical Remaining
1
Simplify the radical
A LaTex expression showing square root of 20d{m to the power of 4 }
a A LaTex expression showing 2{m} to the power of 2 square root of 5d
b A LaTex expression showing 5msquare root of d
c A LaTex expression showing 5msquare root of 2d
d A LaTex expression showing {m} to the power of 2 square root of 4d
e A LaTex expression showing 5msquare root of 8d
2
Simplify the radical
A LaTex expression showing square root of 48x{d to the power of 2 }
a A LaTex expression showing 6{d} to the power of 2 square root of 6x
b A LaTex expression showing 4dsquare root of 3x
c A LaTex expression showing dsquare root of x
d A LaTex expression showing 2dsquare root of x
e A LaTex expression showing 5dsquare root of x
3
Simplify the radical
A LaTex expression showing square root of 50{n to the power of 3 {r} to the power of 2 }
a A LaTex expression showing 5nrsquare root of 2n
b A LaTex expression showing 6{n} to the power of 2 rsquare root of n
c A LaTex expression showing 2nrsquare root of 4n
d A LaTex expression showing 4{n} to the power of 2 {r} to the power of 2 square root of 5{n to the power of 3 }
e A LaTex expression showing 2n{r} to the power of 2 square root of 4n
4
Simplify the radical
A LaTex expression showing square root of 50{z to the power of 2 {m} to the power of 3 }
a A LaTex expression showing 2zmsquare root of 3{m to the power of 3 }
b A LaTex expression showing 4zmsquare root of 2{m to the power of 2 }
c A LaTex expression showing 5z{m} to the power of 3 square root of 3{m to the power of 3 }
d A LaTex expression showing 6zmsquare root of 4{m to the power of 2 }
e A LaTex expression showing 5zmsquare root of 2m
5
Simplify the radical
A LaTex expression showing square root of 32{y to the power of 2 {b} to the power of 5 }
a A LaTex expression showing 2y{b} to the power of 3 square root of 2{b to the power of 2 }
b A LaTex expression showing 4y{b} to the power of 2 square root of 2b
c A LaTex expression showing 3{y} to the power of 3 {b} to the power of 2 square root of b
d A LaTex expression showing 4y{b} to the power of 3 square root of b
e A LaTex expression showing ybsquare root of 5b
6
Simplify the radical
A LaTex expression showing square root of 27{x to the power of 3 {b} to the power of 3 }
a A LaTex expression showing 4{x} to the power of 3 bsquare root of 6{x to the power of 2 {b} to the power of 2 }
b A LaTex expression showing {x} to the power of 2 bsquare root of 5xb
c A LaTex expression showing 3xbsquare root of 3xb
d A LaTex expression showing x{b} to the power of 2 square root of 4{x to the power of 3 b}
e A LaTex expression showing x{b} to the power of 3 square root of 4x{b to the power of 3 }
7
Simplify the radical
A LaTex expression showing square root of 45{y to the power of 3 x}
a A LaTex expression showing {y} to the power of 2 square root of 6{y to the power of 2 x}
b A LaTex expression showing {y} to the power of 2 square root of 7yx
c A LaTex expression showing ysquare root of 7y{x to the power of 3 }
d A LaTex expression showing 3ysquare root of 5yx
e A LaTex expression showing 5{y} to the power of 2 square root of 2y{x to the power of 3 }
8
Simplify the radical
A LaTex expression showing square root of 18{d to the power of 3 {y} to the power of 4 }
a A LaTex expression showing d{y} to the power of 4 square root of 2d
b A LaTex expression showing d{y} to the power of 3 square root of 5{d to the power of 2 }
c A LaTex expression showing dysquare root of d
d A LaTex expression showing 3d{y} to the power of 2 square root of 2d