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

275m3b5\sqrt{275{m}^{3}{b}^{5}}

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 63{x to the power of 5 {r} to the power of 3 }
a A LaTex expression showing 4x{r} to the power of 3 square root of 5xr
b A LaTex expression showing {x} to the power of 3 {r} to the power of 2 square root of 9{x to the power of 3 {r} to the power of 2 }
c A LaTex expression showing 3{x} to the power of 2 rsquare root of 7xr
d A LaTex expression showing x{r} to the power of 2 square root of 3{x to the power of 2 {r} to the power of 3 }
e A LaTex expression showing {x} to the power of 4 rsquare root of 6{x to the power of 3 r}
f A LaTex expression showing 5{x} to the power of 2 rsquare root of 8{x to the power of 3 {r} to the power of 3 }
2
Simplify the radical
A LaTex expression showing square root of 20{x to the power of 3 {m} to the power of 5 }
a A LaTex expression showing 4x{m} to the power of 2 square root of 7xm
b A LaTex expression showing xmsquare root of 6x{m to the power of 2 }
c A LaTex expression showing {x} to the power of 2 {m} to the power of 3 square root of 5x{m to the power of 2 }
d A LaTex expression showing 2x{m} to the power of 2 square root of 5xm
e A LaTex expression showing {x} to the power of 3 {m} to the power of 3 square root of 7{x to the power of 2 {m} to the power of 3 }
f A LaTex expression showing 3x{m} to the power of 3 square root of 8{x to the power of 2 {m} to the power of 2 }
3
Simplify the radical
A LaTex expression showing square root of 20{r to the power of 3 c}
a A LaTex expression showing 5rsquare root of r{c to the power of 3 }
b A LaTex expression showing 2rsquare root of 5rc
c A LaTex expression showing 2rsquare root of 3r{c to the power of 2 }
d A LaTex expression showing 4{r} to the power of 2 square root of 4r{c to the power of 2 }
e A LaTex expression showing 5rsquare root of 3{r to the power of 2 c}
f A LaTex expression showing rsquare root of 3{r to the power of 3 {c} to the power of 3 }
4
Simplify the radical
A LaTex expression showing square root of 176{y to the power of 2 {x} to the power of 2 }
a A LaTex expression showing 7{y} to the power of 3 xsquare root of 9
b A LaTex expression showing 2{y} to the power of 3 {x} to the power of 2 square root of 10
c A LaTex expression showing yxsquare root of 13
d A LaTex expression showing 5y{x} to the power of 2 square root of 8
e A LaTex expression showing 5y{x} to the power of 2 square root of 7
f A LaTex expression showing 4yxsquare root of 11
5
Simplify the radical
A LaTex expression showing square root of 28{r to the power of 2 {b} to the power of 2 }
a A LaTex expression showing rbsquare root of 10
b A LaTex expression showing rbsquare root of 3
c A LaTex expression showing 2{r} to the power of 2 bsquare root of 7
d A LaTex expression showing 2rbsquare root of 7
e A LaTex expression showing 2rbsquare root of 8
f A LaTex expression showing 2{r} to the power of 2 bsquare root of 4
6
Simplify the radical
A LaTex expression showing square root of 20xr
a A LaTex expression showing 2square root of 5xr
b A LaTex expression showing square root of 8{x to the power of 2 r}
c A LaTex expression showing 4square root of 2xr
d A LaTex expression showing square root of 7{x to the power of 3 {r} to the power of 3 }
e A LaTex expression showing 5square root of 7{x to the power of 2 r}
f A LaTex expression showing 4square root of 8xr
7
Simplify the radical
A LaTex expression showing square root of 8r{c to the power of 2 }
a A LaTex expression showing csquare root of 4r
b A LaTex expression showing 5csquare root of 3r
c A LaTex expression showing csquare root of {r to the power of 2 }
d A LaTex expression showing 3{c} to the power of 2 square root of 2{r to the power of 3 }
e A LaTex expression showing 2csquare root of 2r
f A LaTex expression showing 2csquare root of r