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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.

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

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

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Simplify the radical

32â‹…5â‹…x2â‹…p2â‹…\sqrt{3^2\cdot 5\cdot x^2\cdot p^2\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 2 to the power of 2 times 11 times p to the power of 2 times m to the power of 2 times
a A LaTex expression showing 7p{m} to the power of 2 square root of 9
b A LaTex expression showing {p} to the power of 3 msquare root of 8
c A LaTex expression showing 2p{m} to the power of 3 square root of 12
d A LaTex expression showing {p} to the power of 2 msquare root of 10
e A LaTex expression showing 4pmsquare root of 11
f A LaTex expression showing 5pmsquare root of 11
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 c times y times
a A LaTex expression showing 3csquare root of 5cy
b A LaTex expression showing 3csquare root of 5c{y to the power of 3 }
c A LaTex expression showing 4csquare root of 3cy
d A LaTex expression showing 6csquare root of 2{c to the power of 3 y}
e A LaTex expression showing {c} to the power of 2 square root of 6c{y to the power of 2 }
f A LaTex expression showing csquare root of 6c{y to the power of 2 }
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 c to the power of 2 times c to the power of 2 times p to the power of 2 times
a A LaTex expression showing {c} to the power of 3 {p} to the power of 2
b A LaTex expression showing 4{c} to the power of 2 psquare root of 3
c A LaTex expression showing 3{c} to the power of 3 psquare root of 2
d A LaTex expression showing 6{c} to the power of 4 {p} to the power of 3 square root of 3
e A LaTex expression showing 3cp
f A LaTex expression showing 6{c} to the power of 4 p
4
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 11 times r to the power of 2 times r times x times
a A LaTex expression showing 5rsquare root of 10r{x to the power of 3 }
b A LaTex expression showing 3rsquare root of 14{r to the power of 3 x}
c A LaTex expression showing 2rsquare root of 11rx
d A LaTex expression showing rsquare root of 14rx
e A LaTex expression showing rsquare root of 7r{x to the power of 3 }
f A LaTex expression showing {r} to the power of 3 square root of 8rx
5
Simplify the radical
A LaTex expression showing square root of 3 to the power of 2 times 5 times x to the power of 2 times p to the power of 2 times
a A LaTex expression showing x{p} to the power of 2 square root of 7
b A LaTex expression showing 3xpsquare root of 5
c A LaTex expression showing 3x{p} to the power of 2 square root of 2
d A LaTex expression showing 2{x} to the power of 3 psquare root of 3
e A LaTex expression showing {x} to the power of 3 {p} to the power of 2 square root of 7
f A LaTex expression showing {x} to the power of 3 psquare root of 4
6
Simplify the radical
A LaTex expression showing square root of 2 times 3 to the power of 2 times z to the power of 2 times z times d to the power of 2 times d times
a A LaTex expression showing 6{z} to the power of 2 dsquare root of zd
b A LaTex expression showing 4z{d} to the power of 2 square root of 2z{d to the power of 2 }
c A LaTex expression showing 3zdsquare root of 2zd
d A LaTex expression showing 6zdsquare root of {z to the power of 2 {d} to the power of 3 }
e A LaTex expression showing 6{z} to the power of 2 {d} to the power of 3 square root of {z to the power of 2 {d} to the power of 3 }
f A LaTex expression showing 3z{d} to the power of 3 square root of 2{z to the power of 3 d}
7
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 7 times d to the power of 2 times y to the power of 2 times y times
a A LaTex expression showing 2{d} to the power of 2 ysquare root of 6{y to the power of 3 }
b A LaTex expression showing 2dysquare root of 7y
c A LaTex expression showing 3{d} to the power of 3 ysquare root of 8y
d A LaTex expression showing d{y} to the power of 2 square root of 6y
e A LaTex expression showing dysquare root of 5y
f A LaTex expression showing 5dysquare root of 4{y to the power of 2 }