Radicals - Cube - Simplify From Cubed Factors, Values and Variables, Radical Remaining (Level 3)

This math topic focuses on advanced simplification of cube-root radicals, involving both numerical and variable factors with some radicals remaining in the expression. It includes extracting cube-root factors from under the radical when possible, while also dealing with expressions where parts of the radicand are not perfect cubes, leaving them in radical form. The problems explore simplifying cube-root radicals with complex algebraic expressions that include exponents, aiming to foster a deep understanding of radical manipulation and algebraic simplification.

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Cube - Simplify From Cubed Factors, Values and Variables, Radical Remaining

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Simplify the radical

22â‹…11â‹…r2â‹…râ‹…xâ‹…\sqrt{2^2\cdot 11\cdot r^2\cdot r\cdot x\cdot }

Radicals - Cube - Simplify From Cubed Factors, Values and Variables, Radical Remaining Worksheet

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Math worksheet on 'Radicals - Cube - Simplify From Cubed 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 to the power of 2 times 3 times p to the power of 2 times r to the power of 2 times r to the power of 2 times
a A LaTex expression showing {p} to the power of 2 {r} to the power of 4
b A LaTex expression showing 2p{r} to the power of 2 square root of 3
c A LaTex expression showing 4{p} to the power of 3 rsquare root of 5
d A LaTex expression showing prsquare root of 4
e A LaTex expression showing 2p{r} to the power of 4 square root of 3
f A LaTex expression showing 3p{r} to the power of 3 square root of 5
2
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 to the power of 2 times 3 times c to the power of 2 times x times
a A LaTex expression showing 6{c} to the power of 2 square root of 6x
b A LaTex expression showing 2csquare root of 2x
c A LaTex expression showing 4csquare root of 3x
d A LaTex expression showing 5{c} to the power of 3 square root of 5{x to the power of 2 }
e A LaTex expression showing 6{c} to the power of 2 square root of 5{x to the power of 3 }
f A LaTex expression showing 5csquare root of 2x
3
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 to the power of 2 times 3 times z to the power of 2 times z to the power of 2 times b to the power of 2 times b times
a A LaTex expression showing zbsquare root of 6b
b A LaTex expression showing 4{z} to the power of 2 bsquare root of 3b
c A LaTex expression showing 4zbsquare root of 4{b to the power of 3 }
d A LaTex expression showing 6{z} to the power of 2 {b} to the power of 2 square root of 3{b to the power of 2 }
e A LaTex expression showing 7{z} to the power of 4 bsquare root of b
f A LaTex expression showing 2zbsquare root of 2b
4
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 to the power of 2 times 3 times c to the power of 2 times c times y times
a A LaTex expression showing 6csquare root of 2{c to the power of 3 y}
b A LaTex expression showing csquare root of 6c{y to the power of 2 }
c A LaTex expression showing 4csquare root of 3cy
d A LaTex expression showing 3csquare root of 5c{y to the power of 3 }
e A LaTex expression showing 3csquare root of 5cy
f A LaTex expression showing {c} to the power of 2 square root of 6c{y to the power of 2 }
5
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 to the power of 2 times 2 times b to the power of 2 times b to the power of 2 times m to the power of 2 times m to the power of 2 times
a A LaTex expression showing 3b{m} to the power of 3
b A LaTex expression showing 5b{m} to the power of 2 square root of 3
c A LaTex expression showing 5{b} to the power of 4 m
d A LaTex expression showing 4{b} to the power of 2 {m} to the power of 2 square root of 2
e A LaTex expression showing {b} to the power of 3 {m} to the power of 4 square root of 2
f A LaTex expression showing 7bm
6
Simplify the radical
A LaTex expression showing square root of 3 to the power of 2 times 11 times c to the power of 2 times c to the power of 2 times c times y to the power of 2 times y times
a A LaTex expression showing 3{c} to the power of 2 ysquare root of 11cy
b A LaTex expression showing c{y} to the power of 2 square root of 10cy
c A LaTex expression showing cysquare root of 7cy
d A LaTex expression showing {c} to the power of 2 {y} to the power of 2 square root of 10cy
e A LaTex expression showing 2{c} to the power of 2 ysquare root of 12c{y to the power of 2 }
f A LaTex expression showing 5cysquare root of 13{c to the power of 3 {y} to the power of 2 }
7
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 3 times d to the power of 2 times n to the power of 2 times n to the power of 2 times
a A LaTex expression showing 4{d} to the power of 2 nsquare root of 5
b A LaTex expression showing 4{d} to the power of 2 n
c A LaTex expression showing 2d{n} to the power of 2 square root of 3
d A LaTex expression showing d{n} to the power of 3
e A LaTex expression showing 2d{n} to the power of 3 square root of 6
f A LaTex expression showing {d} to the power of 3 {n} to the power of 4