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.

more
View

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

Mobius Math Academy logo
Radicals - Cube - Simplify From Cubed Factors, Values and Variables, Radical Remaining
1
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times 11 times d times y to the power of 2 times
a A LaTex expression showing 5ysquare root of 11d
b A LaTex expression showing 5{y} to the power of 3 square root of 8{d to the power of 2 }
c A LaTex expression showing 6ysquare root of 14d
d A LaTex expression showing 2{y} to the power of 2 square root of 11d
e A LaTex expression showing 3ysquare root of 10{d to the power of 3 }
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 5 times x to the power of 2 times b to the power of 2 times
a A LaTex expression showing {x} to the power of 3 bsquare root of 6
b A LaTex expression showing 4xbsquare root of 5
c A LaTex expression showing 4x{b} to the power of 2 square root of 2
d A LaTex expression showing 7x{b} to the power of 2 square root of 5
e A LaTex expression showing 6x{b} to the power of 2 square root of 5
3
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times 7 times b to the power of 2 times b times m times
a A LaTex expression showing 7bsquare root of 7{b to the power of 2 {m} to the power of 3 }
b A LaTex expression showing 3bsquare root of 10b{m to the power of 2 }
c A LaTex expression showing 5bsquare root of 7bm
d A LaTex expression showing bsquare root of 10bm
e A LaTex expression showing 6{b} to the power of 3 square root of 7{b to the power of 3 m}
4
Simplify the radical
A LaTex expression showing square root of 3 times 5 to the power of 2 times y to the power of 2 times y times z to the power of 2 times
a A LaTex expression showing 6{y} to the power of 3 {z} to the power of 2 square root of 4{y to the power of 3 }
b A LaTex expression showing 5yzsquare root of 3y
c A LaTex expression showing {y} to the power of 3 zsquare root of y
d A LaTex expression showing 3y{z} to the power of 2 square root of y
e A LaTex expression showing 6y{z} to the power of 3 square root of 5y
5
Simplify the radical
A LaTex expression showing square root of 2 times 5 to the power of 2 times d to the power of 2 times y to the power of 2 times
a A LaTex expression showing 6{d} to the power of 2 y
b A LaTex expression showing 5d{y} to the power of 3 square root of 5
c A LaTex expression showing 7d{y} to the power of 3
d A LaTex expression showing 5dysquare root of 2
e A LaTex expression showing dysquare root of 2
6
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 5 times p to the power of 2 times m to the power of 2 times m times
a A LaTex expression showing 2{p} to the power of 2 {m} to the power of 3 square root of 4{m to the power of 2 }
b A LaTex expression showing {p} to the power of 3 {m} to the power of 3 square root of 8m
c A LaTex expression showing 2{p} to the power of 2 msquare root of 3m
d A LaTex expression showing 2pmsquare root of 5m
e A LaTex expression showing 5{p} to the power of 2 msquare root of 8m
7
Simplify the radical
A LaTex expression showing square root of 2 times 3 to the power of 2 times b times z to the power of 2 times z to the power of 2 times
a A LaTex expression showing 2zsquare root of 4{b to the power of 2 }
b A LaTex expression showing 6{z} to the power of 2 square root of {b to the power of 2 }
c A LaTex expression showing 3{z} to the power of 2 square root of 2b
d A LaTex expression showing {z} to the power of 3 square root of 2b
e A LaTex expression showing 4zsquare root of 5b
8
Simplify the radical
A LaTex expression showing square root of 2 times 5 to the power of 2 times n to the power of 2 times n times z to the power of 2 times z times
a A LaTex expression showing 7nzsquare root of nz
b A LaTex expression showing 7n{z} to the power of 3 square root of 4nz
c A LaTex expression showing 7n{z} to the power of 3 square root of 2n{z to the power of 3 }
d A LaTex expression showing 3{n} to the power of 2 zsquare root of nz
e A LaTex expression showing 5nzsquare root of 2nz