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Radicals - 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

5â‹…5â‹…7â‹…xâ‹…xâ‹…câ‹…c\sqrt{5\cdot 5\cdot 7\cdot x\cdot x\cdot c\cdot c}

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 5 times 5 times 11 times p times m times m
a A LaTex expression showing 6msquare root of 14{p to the power of 2 }
b A LaTex expression showing 5msquare root of 13p
c A LaTex expression showing 2{m} to the power of 3 square root of 11{p to the power of 2 }
d A LaTex expression showing 5msquare root of 11p
e A LaTex expression showing 2{m} to the power of 3 square root of 14{p to the power of 2 }
f A LaTex expression showing 8{m} to the power of 2 square root of 7p
2
Simplify the radical
A LaTex expression showing square root of 3 times 3 times 5 times d times d times n times n
a A LaTex expression showing 3dnsquare root of 5
b A LaTex expression showing 4d{n} to the power of 3 square root of 6
c A LaTex expression showing 5d{n} to the power of 3 square root of 3
d A LaTex expression showing d{n} to the power of 2
e A LaTex expression showing {d} to the power of 2 {n} to the power of 2 square root of 5
f A LaTex expression showing {d} to the power of 2 nsquare root of 3
3
Simplify the radical
A LaTex expression showing square root of 3 times 3 times 11 times n times n times n times n times n times b
a A LaTex expression showing 2{n} to the power of 3 square root of 11{n to the power of 2 b}
b A LaTex expression showing 3{n} to the power of 3 square root of 7n{b to the power of 2 }
c A LaTex expression showing 6nsquare root of 10nb
d A LaTex expression showing 3{n} to the power of 2 square root of 11nb
e A LaTex expression showing 6nsquare root of 7nb
f A LaTex expression showing 2nsquare root of 11{n to the power of 3 b}
4
A LaTex expression showing square root of 2 times 2 times 2 times 2 times 5 times c times n times n times n times n times n
Simplify the radical
a A LaTex expression showing 3{n} to the power of 2 square root of 6cn
b A LaTex expression showing 5nsquare root of {c to the power of 2 {n} to the power of 2 }
c A LaTex expression showing 4{n} to the power of 2 square root of 5cn
d A LaTex expression showing 2nsquare root of 5c{n to the power of 3 }
e A LaTex expression showing {n} to the power of 2 square root of 2c{n to the power of 2 }
f A LaTex expression showing 7{n} to the power of 2 square root of 8cn
5
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 2square root of 4{n to the power of 3 b}
c A LaTex expression showing 3square root of 5nb
d A LaTex expression showing square root of nb
e A LaTex expression showing square root of {n to the power of 2 b}
f A LaTex expression showing 2square root of 2nb
6
Simplify the radical
A LaTex expression showing square root of 5 times 5 times 7 times x times x times c times c
a A LaTex expression showing 8xcsquare root of 10
b A LaTex expression showing 5xcsquare root of 7
c A LaTex expression showing 6x{c} to the power of 2 square root of 3
d A LaTex expression showing 8{x} to the power of 3 {c} to the power of 3 square root of 4
e A LaTex expression showing 3{x} to the power of 2 csquare root of 8
f A LaTex expression showing 5x{c} to the power of 3 square root of 9
7
Simplify the radical
A LaTex expression showing square root of 3 times 5 times 5 times m times m times m times p
a A LaTex expression showing msquare root of 5mp
b A LaTex expression showing 4msquare root of {m to the power of 3 p}
c A LaTex expression showing 4msquare root of 3{m to the power of 2 p}
d A LaTex expression showing 5msquare root of 3mp
e A LaTex expression showing 3msquare root of 4{m to the power of 2 {p} to the power of 2 }
f A LaTex expression showing 7msquare root of {m to the power of 3 p}