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.

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

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Radicals - Cube - Simplifying from Factors, Values and Variables, Radical Remaining
1
Simplify the radical
A LaTex expression showing square root of 5 times 5 times 7 times c times c times n times n times n times n times n
a A LaTex expression showing 7{c} to the power of 2 {n} to the power of 3 square root of 10n
b A LaTex expression showing cnsquare root of 4{n to the power of 2 }
c A LaTex expression showing 5c{n} to the power of 2 square root of 7n
d A LaTex expression showing 7c{n} to the power of 2 square root of 3n
e A LaTex expression showing 6{c} to the power of 3 nsquare root of 8{n to the power of 3 }
2
Simplify the radical
A LaTex expression showing square root of 3 times 3 times 7 times d times d times d times m
a A LaTex expression showing dsquare root of 3dm
b A LaTex expression showing 4dsquare root of 8{d to the power of 2 {m} to the power of 3 }
c A LaTex expression showing dsquare root of 7dm
d A LaTex expression showing 3dsquare root of 7dm
e A LaTex expression showing 4dsquare root of 7{d to the power of 2 m}
3
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 3 times c times r
a A LaTex expression showing 3square root of 6{c to the power of 3 r}
b A LaTex expression showing 4square root of {c to the power of 3 r}
c A LaTex expression showing 2square root of 3cr
d A LaTex expression showing 5square root of {c to the power of 2 r}
e A LaTex expression showing square root of c{r to the power of 2 }
4
A LaTex expression showing square root of 2 times 5 times 5 times n times n times n times n times n times x times x times x times x times x
Simplify the radical
a A LaTex expression showing 5n{x} to the power of 4 square root of 3{n to the power of 3 {x} to the power of 3 }
b A LaTex expression showing 8{n} to the power of 2 xsquare root of {n to the power of 2 {x} to the power of 3 }
c A LaTex expression showing 5{n} to the power of 2 {x} to the power of 2 square root of 2nx
d A LaTex expression showing 2{n} to the power of 2 xsquare root of 2{n to the power of 2 x}
e A LaTex expression showing 5{n} to the power of 4 {x} to the power of 2 square root of 2{n to the power of 3 x}
5
Simplify the radical
A LaTex expression showing square root of 5 times 5 times 7 times d times d times d times c times c times c times c
a A LaTex expression showing 5d{c} to the power of 4 square root of 9d
b A LaTex expression showing 7{d} to the power of 2 csquare root of 5d
c A LaTex expression showing 3d{c} to the power of 4 square root of 6d
d A LaTex expression showing 6dcsquare root of 3d
e A LaTex expression showing 5d{c} to the power of 2 square root of 7d
6
A LaTex expression showing square root of 2 times 2 times 2 times 2 times 11 times b times b times b times d times d times d times d times d
Simplify the radical
a A LaTex expression showing 2b{d} to the power of 4 square root of 7bd
b A LaTex expression showing {b} to the power of 3 {d} to the power of 3 square root of 8b{d to the power of 3 }
c A LaTex expression showing 5{b} to the power of 2 {d} to the power of 2 square root of 11bd
d A LaTex expression showing 4b{d} to the power of 2 square root of 11bd
e A LaTex expression showing 3{b} to the power of 2 {d} to the power of 4 square root of 11{b to the power of 2 {d} to the power of 2 }
7
A LaTex expression showing square root of 3 times 3 times 7 times c times c times c times c times p times p times p times p times p
Simplify the radical
a A LaTex expression showing 5{c} to the power of 3 psquare root of 6p
b A LaTex expression showing 3{c} to the power of 2 {p} to the power of 2 square root of 7p
c A LaTex expression showing {c} to the power of 3 {p} to the power of 3 square root of 9p
d A LaTex expression showing c{p} to the power of 2 square root of 4{p to the power of 2 }
e A LaTex expression showing 5{c} to the power of 3 {p} to the power of 4 square root of 4{p to the power of 2 }
8
Simplify the radical
A LaTex expression showing square root of 2 times 2 times 2 times d times d times y times y times y times y times y
a A LaTex expression showing 2{d} to the power of 2 ysquare root of 4y
b A LaTex expression showing d{y} to the power of 4 square root of 5y
c A LaTex expression showing 5d{y} to the power of 2 square root of y
d A LaTex expression showing 2d{y} to the power of 2 square root of 2y
e A LaTex expression showing 2dysquare root of {y to the power of 3 }