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Radicals - 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.

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Cube - Simplifying, Values and Variables, Radical Remaining

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Simplify the radical

175n3m3\sqrt{175{n}^{3}{m}^{3}}

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

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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 80{y to the power of 2 p}
a A LaTex expression showing ysquare root of 5p
b A LaTex expression showing {y} to the power of 2 square root of 7p
c A LaTex expression showing 2ysquare root of 5{p to the power of 3 }
d A LaTex expression showing 7ysquare root of 3{p to the power of 2 }
e A LaTex expression showing 4ysquare root of 5p
f A LaTex expression showing 6ysquare root of 4p
2
Simplify the radical
A LaTex expression showing square root of 175nx
a A LaTex expression showing 5square root of 8{n to the power of 3 x}
b A LaTex expression showing 5square root of 7nx
c A LaTex expression showing 8square root of 3{n to the power of 2 {x} to the power of 3 }
d A LaTex expression showing 6square root of 7nx
e A LaTex expression showing 7square root of 6n{x to the power of 2 }
f A LaTex expression showing 8square root of 10nx
3
Simplify the radical
A LaTex expression showing square root of 20xr
a A LaTex expression showing square root of 8{x to the power of 2 r}
b A LaTex expression showing 5square root of 7{x to the power of 2 r}
c A LaTex expression showing 2square root of 5xr
d A LaTex expression showing 4square root of 8xr
e A LaTex expression showing square root of 7{x to the power of 3 {r} to the power of 3 }
f A LaTex expression showing 4square root of 2xr
4
Simplify the radical
A LaTex expression showing square root of 20{n to the power of 2 {c} to the power of 5 }
a A LaTex expression showing ncsquare root of 7c
b A LaTex expression showing 2n{c} to the power of 2 square root of 5c
c A LaTex expression showing ncsquare root of 7{c to the power of 3 }
d A LaTex expression showing n{c} to the power of 2 square root of 5{c to the power of 2 }
e A LaTex expression showing n{c} to the power of 4 square root of 7c
f A LaTex expression showing n{c} to the power of 4 square root of 5c
5
Simplify the radical
A LaTex expression showing square root of 112{p to the power of 2 {d} to the power of 5 }
a A LaTex expression showing 2{p} to the power of 3 {d} to the power of 2 square root of 9{d to the power of 3 }
b A LaTex expression showing 4p{d} to the power of 2 square root of 7d
c A LaTex expression showing 4pdsquare root of 4d
d A LaTex expression showing 6{p} to the power of 2 {d} to the power of 3 square root of 4{d to the power of 3 }
e A LaTex expression showing 5p{d} to the power of 3 square root of 3d
f A LaTex expression showing p{d} to the power of 2 square root of 4{d to the power of 3 }
6
Simplify the radical
A LaTex expression showing square root of 50{b to the power of 3 {x} to the power of 3 }
a A LaTex expression showing 7bxsquare root of 2b{x to the power of 2 }
b A LaTex expression showing 2b{x} to the power of 2 square root of 2{b to the power of 2 {x} to the power of 2 }
c A LaTex expression showing 3bxsquare root of 2bx
d A LaTex expression showing 5bxsquare root of 2bx
e A LaTex expression showing 8b{x} to the power of 2 square root of b{x to the power of 3 }
f A LaTex expression showing 8{b} to the power of 3 xsquare root of 5bx
7
Simplify the radical
A LaTex expression showing square root of 63{c to the power of 5 {n} to the power of 4 }
a A LaTex expression showing 4c{n} to the power of 2 square root of 4c
b A LaTex expression showing 2c{n} to the power of 4 square root of 9c
c A LaTex expression showing 6{c} to the power of 4 nsquare root of 10c
d A LaTex expression showing 5cnsquare root of 3c
e A LaTex expression showing 2{c} to the power of 4 {n} to the power of 3 square root of 5c
f A LaTex expression showing 3{c} to the power of 2 {n} to the power of 2 square root of 7c