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Radical

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

This math topic focuses on simplifying cube radicals involving factors, values, and variables, with some radicals possibly remaining. It is a higher-level practice within the broader unit of advanced simplification of radicals. Students are required to simplify complex radical expressions which include numbers and different powers of variables. Multiple-choice answers are provided, requiring careful manipulation of radical and algebraic rules to determine the correct simplifications. The complexity of the problems advances with each question, enhancing students' skills in handling higher degrees of algebraic expressions under radical signs.

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

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Cube - Simplifying from Factors, Values and Variables, Radical Remaining

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Simplify the radical

2⋅3⋅3⋅x⋅z⋅z⋅z⋅z⋅z\sqrt{2\cdot 3\cdot 3\cdot x\cdot z\cdot z\cdot z\cdot z\cdot z}

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

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Math worksheet on 'Radicals - Cube - Simplifying from Factors, 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 2 times 2 times 2 times 2 times 2 times r times r times p
a A LaTex expression showing 5rsquare root of p
b A LaTex expression showing 7rsquare root of {p to the power of 2 }
c A LaTex expression showing 4rsquare root of 2p
d A LaTex expression showing 2rsquare root of p
e A LaTex expression showing 5rsquare root of {p to the power of 2 }
f A LaTex expression showing 2{r} to the power of 2 square root of {p to the power of 2 }
2
A LaTex expression showing square root of 2 times 2 times 2 times 2 times 2 times z times z times z times z times x times x times x
Simplify the radical
a A LaTex expression showing 7{z} to the power of 2 xsquare root of 2{x to the power of 2 }
b A LaTex expression showing 2zxsquare root of {x to the power of 3 }
c A LaTex expression showing {z} to the power of 4 xsquare root of 5{x to the power of 3 }
d A LaTex expression showing 5zxsquare root of x
e A LaTex expression showing 4{z} to the power of 2 xsquare root of 2x
f A LaTex expression showing 2zxsquare root of 5x
3
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times n times b
a A LaTex expression showing 2square root of 2{n to the power of 2 {b} to the power of 3 }
b A LaTex expression showing square root of {n to the power of 2 b}
c A LaTex expression showing square root of nb
d A LaTex expression showing 3square root of 5nb
e A LaTex expression showing 2square root of 4{n to the power of 3 b}
f A LaTex expression showing 2square root of 2nb
4
A LaTex expression showing square root of 3 times 3 times 11 times x times x times x times m times m times m times m times m
Simplify the radical
a A LaTex expression showing 3xmsquare root of 10xm
b A LaTex expression showing {x} to the power of 3 {m} to the power of 3 square root of 11{x to the power of 2 m}
c A LaTex expression showing 2x{m} to the power of 3 square root of 8{x to the power of 2 {m} to the power of 2 }
d A LaTex expression showing 3x{m} to the power of 2 square root of 11xm
e A LaTex expression showing x{m} to the power of 2 square root of 10{x to the power of 2 m}
f A LaTex expression showing 2x{m} to the power of 4 square root of 13x{m to the power of 3 }
5
A LaTex expression showing square root of 2 times 5 times 5 times r times r times r times r times m times m times m
Simplify the radical
a A LaTex expression showing 5rmsquare root of 2m
b A LaTex expression showing 4{r} to the power of 2 msquare root of 4{m to the power of 2 }
c A LaTex expression showing 3r{m} to the power of 3 square root of m
d A LaTex expression showing 3rmsquare root of 5m
e A LaTex expression showing 5{r} to the power of 2 msquare root of 2m
f A LaTex expression showing 5{r} to the power of 4 msquare root of {m to the power of 3 }
6
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 5 times p times p times b times b times b times b times b
a A LaTex expression showing 4pbsquare root of 2b
b A LaTex expression showing 5{p} to the power of 2 {b} to the power of 4 square root of b
c A LaTex expression showing 2p{b} to the power of 2 square root of 5b
d A LaTex expression showing 3{p} to the power of 3 bsquare root of 6b
e A LaTex expression showing {p} to the power of 3 bsquare root of 6{b to the power of 2 }
f A LaTex expression showing 4{p} to the power of 3 {b} to the power of 2 square root of 3{b to the power of 3 }
7
Simplify the radical
A LaTex expression showing square root of 3 times 3 times 3 times n times n times n times p times p times p
a A LaTex expression showing {n} to the power of 2 psquare root of np
b A LaTex expression showing {n} to the power of 2 psquare root of 3n{p to the power of 3 }
c A LaTex expression showing 3npsquare root of 3np
d A LaTex expression showing 2{n} to the power of 3 {p} to the power of 2 square root of {n to the power of 2 p}
e A LaTex expression showing 4n{p} to the power of 2 square root of 2{n to the power of 2 {p} to the power of 3 }
f A LaTex expression showing 3{n} to the power of 2 {p} to the power of 2 square root of 3n{p to the power of 3 }